There aren't many weapons that would be useful in any stratum, but I'd say Leviathan Blade + Polaris would be a nice choice. Polaris can help you safely and quickly deal with all kinds of constructs (except for mecha knights probably but Levi charge destroys those easily), undead and, if you can spread shots, devilites. Levi can take care of the rest.
Divine Avenger + Gran Faust is a good combo for pure swordie, but destroying gun puppies/howlitzers/polyps in arenas can become a problem since your only ranged option (Divine Avenger charge) would require charging, and charging a weapon is pretty hard with all those projectiles flying around. And fighting against devilite crowds... Ow.
You might also consider Fang of Vog for T2 runs (its devastating charge will save you a lot of time; using it in T3 might not be worth the health loss even with full Vog Cub), Shivermist Buster (soloing T3 devilite levels without it might be troublesome for a beginner, and it's really useful for Vanaduke) and Final Flourish/Barbarous Thorn Blade (pops wolvers and devilites like balloons).

Leviathan Blade [CTR] + Valiance [ASI] = pretty much decent on everything.

brandish (any line except cautery sword) is the underrated sword. But I really love the charge attack.

Flourish/Barbarous Thorn Blade + Polaris would be the best. Both do pure and very high damage. No enemies will be resistant to BOTH weapons, it's also 1 melee + 1 ranged which is useful too.
Forgot to mention they also work good for lockdown.

Sellinstuff, I am also loving the Twisted Snarbie/Gigawatt Pulsar combo right now since each of them is kinda two weapons in one. IMHO letting Pulsar grenades hit before they arm is seriously underrated. Not only is it more polite to team mates, but their sword damage will VASTLY outweigh the lost blast damage. I also went for Pierce sword first because it's the only one not split with Normal and because I like the Snarbie's style.

Kolela, I also intend to go Brandish for my Elemental and Shadow sword needs rather than Sealed Sword, because I prefer "attack" (read: shield/movement) speed to damage AND prefer the looks of the 4- and 5-star Brandishes to their Sealed Sword counterparts. Also, status effects FTW! ...unless they have a chance to backfire. Maybe this is an example of great minds thinking alike.

DMuk, there is no single best set of weapons for that armor and shield. They favour swords, obviously. More specifically, I think that Vog Cub slightly favours the Sealed Sword upgrades over Brandish upgrades while that shield slightly favours the Brandish upgrades over Sealed Sword upgrades. Those "objective" statistical biases for some swords over others are much less important than your personal play style and what you feel comfortable with, though.

I am going two-slot as well since I would rather spend precious resources on gear I can keep than on monthly slot rental- at least while there are still toys I want but do not have, which I expect to be for a long time yet. I think that going two-slot encourages working toward multiple loadouts for different strata much more than 3- or 4-slot, so I cannot recommend a single pair of weapons even for your specific armor and shield and would probably take any such recommendation with a big grain of salt. You will almost certainly need more than two weapons so you can choose two based on stratum.

Also, it might be really hard to specialise in swords (or any class, for that matter) with only two slots. I cannot speak from my own experience, but most recommendations I've seen from experienced specialists on this forum and the wiki include advice to carry at least one backup weapon of a different class so you have at least one sword (for gunners and bombers) and at least one gun or bomb (for sword users) unless you always play in a reliable party that understands your specialisation. Sometimes, it's just not practical to get close to a target and other times it's not reliably possible to avoid getting close. For examples of the former, I've seen a group of turrets spewing more projectiles down a narrow hallway than I could hope to shield against, and heard of turrets surrounded by spikes or brambles. Sometimes, there is a "wrong" class for the situation just like there are "wrong" damage types for monsters. With two slots, carrying a gun means you have to either give up the huge advantage of using the best damage type, or eat the penalty of having to attack with a weak damage type against a two of three monster families, or eat the penalty of using a "weak" weapon class for your specialised armor. All of those are pretty harsh, so you need to play in a well-balanced party or become really REALLY good at the game.

On top of that, wickedly stacked sword bonuses come at a cost to defense, and swords are probably the most risky weapon type to use since you mostly have to get close to your target, so you're building a real glass hammer. If you know what you're doing, you'll wreak havoc like no one else can. If you don't, no party able to support that role will want to play with you since you'd be going through health like cotton candy. I wish you good luck, and if you can pull it off without a backup gun or bomb (or without swords for at least two damage types) my hat's off to you.

If you always prefer a sword against all enemies, or at least close to that, and have a really good party to roll with, then it's a no-brainer. Just get yourself your favourite sword of each specialised damage type as recommended by JDavis, equip two at a time as you please and disregard all of my post after this paragraph because just about any choices are good if that's your style. As jdavis said, the same goes for the other two classes. That specialised armor exists for a reason, and is perfectly viable if it fits your style and, since you only use two weapons at a time, also your party composition. The main sword options for Piercing damage are the Snarble Barb and Flourish lines. Furious Flamberge has a chance to inflict fire, which is generally considered better than Fearless Rigadoon's stun, but it's debated whether the fire or the better base damage of Final Flourish is better. I read that Barbarous Thorn Blade is identical to Final Flourish except for the charge attack; all the Flourishes have a big lunging affair that leaves you wide open but utterly devastates a single target if you connect, while the Thorn Blade pushes you back away from your target and sprays a few barbarous projectiles in a wide spread; better against mobs, still effective against single targets but only very close, and safer than Flourish' berserk flurry in exchange for less total damage. For Elemental damage, the main options are the Divine Avenger (Sealed Sword line) and the status-inflicting Brandish upgrades. DA seems more popular, has slower but heavier hits, and its charge attack is a wicked ranged attack with a wide spread that pushes targets. Brandish upgrades come in three status-inflicting flavours: shock, fire, and freeze. They only inflict status effect with the charge attack, so no worries about the slimes that are healed and supercharged by those effects. They don't hit as hard as DA but are much faster and you can swing twice and still shield quickly, while the DA only lets you swing once at a time without leaving yourself vulnerable. For Shadow damage, the main options seem to be Gran Faust and Acheron. The difference is mostly just like that between Divine Avenger and the other Brandish upgrades, except that the slow one gets the status effect instead- Curse, though with a chance to cast it on you. Fang of Vog is an Elemental sword coveted by many, but as a 5-star Vanaduke token reward, the only way you're likely to get it is by beating the endgame boss several times. That probably puts it beyond the scope of this thread. Its charge attack also has a chance to set you on fire. As a two-slot sword specialist, just get one for each damage type-whichever you think is coolest, really, and you're set.

On the other hand, IF you didn't already know exactly what you're getting into, then you may have some difficult choices to make. I myself prefer to mix both damage type and class, and there seems to be no right or wrong about it in terms of viability, but gunners and bombers usually still like to have a sword for close defense and general single-target DPS while swordmen usually like a gun or maybe bomb for reasons described above. It's not an absolute thing, but important to consider and costs a lot to do if you only have two slots.

I disagree with Jdavis about one (and only one) thing in this thread; the rest is solid advice for players in general, IMHO. If I am using my Twisted Snarbie against Gremlins because my other weapon is Elemental, then whether the Elemental weapon is a Shockburst Brandish or Kilowatt Pulsar has no bearing whatsoever on how restricted I am here. You can imagine any example enemy and weapon pair you like; if I only have one weapon that is viable, then I only have one weapon that is relevent to the situation. Whatever else I brought is only relevent to other situations! On the other hand, if I have one of the optimal damage type and one of the neutral type, I have two viable options; if they are both pretty much the same otherwise, I basically only have one sane choice. The only time weapon class has some bearing on how much freedom I feel I have, is when I have multiple viable options. In that case, having multiple classes to choose from is obviously less restricting. The more different they are in mechanics, the more this will mean. (There IS a world of difference between a Sudaruska and a Dread Venom Striker, but there's two worlds of difference between either of them and a Callahan.)

I think this may be a large part of why Normal damage weapons with specialised counterparts (for example, Neutraliser vs. Biohazard) are not considered garbage when we can always have two specialised damage types; I benefit greatly from being able to use either a gun or other weapon as the situation calls for it, where they are both viable, to the extent I am almost as averse to using only one class as I am to using only one damage type. I can understand that for many players the marginal values of one more damage type and one more weapon class increase a lot more going from one to two than from two to three, so I can see the appeal of a Normal damage weapon for a 3-weapon loadout even if I would prefer a much different approach if I had 3 slots. Buying a third or even fourth slot allows you to do both if you can p[l]ay enough to afford the monthly cost, and makes specialising in one class a lot more viable since you can cover two damage types with your "strong" weapon class AND have a neutral weapon of a second class that never eats a damage penalty. With two slots, you have to choose between the flexibility and the bonus damage OR avoid having a dominant weapon type altogether.

Simple. Levi and Polaris. So am I just guessing at this and pulling out numbers and calculations along with guesses of what should work and what should not? Not at all, since this these are the two weapons that have never left my loadout. They may not be ideal, but then again, with two weapons only, what is? But by far, this has been the best combination i've found. And is not really the damage they provide or the non shadow/elemntal/piercing or whatever or if they do have it, but it's simply the ability that allows you to take on just about ANY type scenario you throw at it.

In full vog, the sword is fast enough that fiends is the only thing you will have some problems with. But along with the gun and some careful hit and run techniques, even those are doable. The most important aspect of the levi is charge attack. This is not only used offensively but alot of times, i used defensively. Once you learn when to go in and do triple damage on stationary enemies, separate healers, kite crowds effectively for max charge damage and three hit cancel along with two hit knockback, the levi is truly an amazing sword.

As for the gun, it covers everything the levi cant like gunning spamming it on a choke of a fiend level, taking out far gun puppies, and especially those OP giant lichen colonies or when you see four lumber closing in on you.

The only situation really that i dont see myself with my polaris and levi if i only had two slots is a t3 fiend level. If i had to pick, i'd probably would have to do shivermist/barb blade or polaris/barb blade. But then again, when i do go into that situation, my vog comes off and serpahic comes on along with skelly shield. But that's another thread ;)

without switching?

i'd say levi (total calibur line) and a polaris to take out gunpuppy's

I'm aiming to get a Leviathan/Graviton Bomb combination, because, well, the bomb does the herding for the Leviathan easily. And it does damage as well.