Well, well, well, isn't that a hipster loadout? I think you can make something really interesting with that mix of gear ya got there. Brandishes are tried-and-true weapons and the rest aren't terrible, they're usable, but they just aren't great (Winmillion particularly so). They're also pretty charge heavy.
From my experience, we got a few options:
-Take some of the weapons, craft some new ones, and move into one of the more standard archetypes (would probably be bomber). You'd focus on a certain playstyle, but you could find a way to incorporate some of the other weapons.
or
-Keep your weapons and start working towards the Chaos set. It offers a universal ctr and dmg low to every weapon with each piece and it's one of the 5*s of the Magic line, and from what I can gather, pretty close to the way you play. It will make your current weapons go well together. The catch is that it doesn't get any offensive bonus until 5*, has mediocre defense, and has an innate weakness to fire, freeze, shock, poison, and curse. If you know how to avoid damage well, the defense doesn't matter, but it's something to consider.

"Why are armors without normal defense a good idea?"
I said the contrary (perhaps you mistyped?) : you shouldn't take an armor without normal defense. The reason is that even in T3, most things do some normal damage. If you look at the damage for any given strata in T3, it will generally be something like about 40% normal, about 50% of a special damage and the 10% of another damage (I just made up those numbers, but that should give you an idea).

So the ideal is to protect against from normal + the special damage you are going to encounter. Since you can't do an armor for each damage yet (too expensive), let's look at the 3 special damage :
- elemental is very present, as there are constructs everywhere. Constructs and gremlins are dangerous, so you should at least take some elemental protection. Good thing : it's easy to get : the bomber armor is only elemental, and both swordsman and gunner sets have an elemental option.
- shadow is a bit more rare. It's for fiends and undeads. While undeads are generally easy especially zombies, fiends are the most difficult. You can avoid fiends for now, be very careful around them or get some shadow armor. Sadly, the bombers don't have any shadow armor, the swordsman one is out of reach for now. Only the gunners have Shadowsun.
- piercing is from beasts and jellies. Unless you run RJP a lot, those are the least difficult mobs. That's why a lot of persons don't wear any piercing resistance. There are some exception (Compound 42 danger mission), but for now you probably don't need any piercing resistance.

As for Silvermail + Heavy Demo Helm : for now, that would make a set that have a bit of every resistance, but in the long term, silvermail is going to be useless. Is that really what you want ? There are better sets, like the Divine Veil + Skolver Darkbrady talked about. Divine Veil is one of the rare armor without normal that is still kinda useful : very few armors have shock resistance, and there are several occasions on which shadow + elemental are mixed in a strata.

As for the weapons, as I said before, any brandish sword is going to work well. An electron vortex wouldn't be my first choice because it isn't very good before it reaches 5*, and it's kinda hard and dangerous to use. The catalyzer wouldn't be in my choices either. You are probably going to regret doing it.

Whatever you choose, remember that you either need at least one normal weapon OR two non-normal weapons (the latter being more desirable), to be able to have normal or strong damage against every family.

To get a more accurate gauge of your defences, look at your overlay (in tab) at the bottom of your character window and it'll show you combined totals from all your armour and UVs.

Beast:high is the same as all damage:high, so there's often little reason to aim for that. A piercing blade generally suits you better, especially with damage bonuses. You can get more detailed answers, ofc, but that's a summary.

If you plan to go for bombs only, you may want to reconsider for now.

I hate to say it, but most bombs really reach their potential at 5*, meaning up until then, it's going to suck : the difference in radius before 5* really makes a big difference, and the vortex bombs really are different at 5* (despite the visible radius not improving). Also, before reaching the end-game, places where bombs are very effective, meaning crowds, are few.

Anyway, if you still want to go that path : Electron Vortex is not a damage bomb. Sure it does some damage, but not enough to be considered a full damage bomb. Here are the damage bombs :
- Nitronome : great for solo or with a party which appreciate it. It has the advantage of being normal, so you won't have any trouble with multiple damage.
- Dark Briar Barrage, as you listed, is the go-to piercing bomb. Works well in a party, as well as against normal targets.
- if you have the OCH, Dark Retribution is a good shadow bomb. Otherwise you'll find your shadow bomb options limited. The vortex one is not meant to damage, really.
- for elemental, you are out of luck too, because most are status weapon. On the other hand, the Ash of Agni + Voltaic Tempest is great to have shock as elemental + some fire (specific resistance) on floors that doesn't resist either (sadly, the go-to late game farming place, FSC, is resistant to fire).
- lastly, I'll reluctantly include the shards/splinters bombs. They have every special damage listed before, but are a little underwhelming, because of their mechanism. I can't really advise getting any of those, I'm pretty sure Nitronome will do better in almost every situation, and the other bomb I talked about WILL do better.

As said Darkbrady, DBB don't really profit from the vortex. I can't think of any bomb which really profit of the vortex, actually (apart from the old RSS, but ... let's forget about our beloved dead RSS).

In my eyes, a bomber is either get a Nitronome and resign yourself to play only solo/ with mates or be prepared to spend a lot of money getting all the other bombs (DBB, DR, AoA, VT are a minimum for me, with a vortex being the finishing touch, add Shivermist for FSC).

P.S. : people here generally like to help beginners who have thought a little about what they want to do and are able to describe their situation. A post like that is bound to have lots of good answers.

I'd have to concur with Bopp/Fradow, that bombing as a beginner is hard. I did it (and did it when RSS was useful) and still found myself more or less incapable of soloing. Once you've maxed your gear off you can solo bosses and all the rest, but w/ <4* bombs, the CWs are pretty rough for anyone without a party to back them up. If you want to go the bombing route, it tends to be better to get one or two hazes and maybe one dps bomb; focus on them and max them off ASAP so you can be increasingly more productive, then once you have a few 5*s, the rest will come naturally.
If you do go that route, I'd suggest shiver or VT as they're useful support bombs. VV is the support bomb, but won't serve you well w/o any oither options, and certainly not so much before 5*.

Also, @Fradow:
With vortexes, I've been playing with alternating between a vortex and shard to try and beef up the damage rates with that; guarantee they get hit and negate that infuriating shard KB. IT works....well enough, but the hit limit gimps it completely from being competitive with your party members. I did feel more useful than just dropping shards alone, though, as every single shard bomb got put to full use; the damage is much more noticeable thatw ay, I find, than using them alone and having half the enemies KBd, half walk away and the other half only take a single hit.

Yes, three halves.

The conventional wisdom is that the shard bombs need no more testing; they are just bad. If you want a piercing damage bomb, go with Dark Briar Barrage. If you want a shadow damage bomb, go with Dark Retribution (if you can get OCH). Otherwise, go with Nitronome or resign yourself to spreading status or vortices.

I have faith that the game designers know and love this game far better than the players. So I suspect that there is some cool tactical niche that the shards bombs must fill. But nobody's really been able to find it, despite trying pretty hard. It doesn't help that the old RSS was a lot of fun, offering a play style that is no longer available in bombs.