Best Weapon

I'm pretty new to this game, but i read some of the wiki, including the sword, gun, shield and bomb guides. I'm, thinking ahead now and asking what is the best sword and gun combo for completing the entire game that you can get from the Hall of Heroes? I'm not looking for an answer like it depends on your playing style, but what weapons would you chose if u had to complete the whole entire game with them?

Just one set for everything? Probably volcanic pepper box and winmillion. Pepper box does all the requisite damage and benefits from gunner armor while winmillion offers me the ability to control my environment and chase down enemies.
Armor setup would be Seerus + Black Kat, with omega shell. Sprite would be mask with handgun ctr perk. Trinkets would be damage. Or health.

You said only hall of heroes, not exactly good if you want a single set, most really good armors come from basil or other means
But from my recommendations the hall of heroes stuff Includes iron slug, dread skelly shield, callahan, maskeraith with either gun ctr or swift steps 2
For non hall of heroes I would say iron slug, warmaster rocket hammer, seerus mask, either mercurial mail or sacred grizzly pathfinder, dread skelly shield, maskeraith (same perks)(have an elite normal harness if you need to only pick one)
For additional weapon slots there's Callahan and winter grave
Trinkets go with a handgun ctr and a pent heart pendant

What sword should I use with the shocking pulsars?
Also is shade helmet, wolver coat, and owlet shield a good pairing?

What sword should I use with the shocking pulsars?
I see that you didn't follow our suggestions about guns to use. That's okay. :)
Those guns are elemental. You don't want to carry only elemental weapons, because then you are mediocre against slimes and fiends, and downright bad against beasts and gremlins. You want your other weapon to be non-elemental. I recommend Acheron. (This is all covered in my sword guide linked above.)
Also is shade helmet, wolver coat, and owlet shield a good pairing?
As I mention in my sword guide linked above, you should always plan in terms of 5-star equipment, because you don't want to invest in an alchemy line that leads somewhere bad. But the items you mention lead entirely to good outcomes (although I would steer away from Snakebite helmets and the Omegaward shield). So it sounds like a fine start. Just start thinking about where you're going with them. For example, Firefly Shade, Vog Cub, and Grey Owlite would be a pretty nice set for much of the endgame content, such as Firestorm Citadel.

The Volcanic Pepperbox, Nitronome, and Leviathan Blade are the best weapons if you plan on getting the least number of weapons to complete the game since they have no drawbacks from any monster family.
The best thing to do is to amass a large arsenal of dozens of weapons, in fact one could go as far to say that a varied backpack of weapon choices is the greatest weapon in the game.
@ Bopp
With Silversaps being a HUGE problem, (one hit punishable with death) the Omegaward is definitely not a bad choice. For armor you want sets that match up type damage and status resistances in order to get the most from them rather than having mediocre status and damage resists all around.

The Volcanic Pepperbox, Nitronome, and Leviathan Blade are the best weapons if you plan on getting the least number of weapons to complete the game since they have no drawbacks from any monster family. The best thing to do is to amass a large arsenal of dozens of weapons, in fact one could go as far to say that a varied backpack of weapon choices is the greatest weapon in the game.
That's not bad advice, but the original poster is specifically asking about one sword and one gun.
Omegaward is definitely not a bad choice
I agree that it is not a bad choice. I said that his current paths "lead entirely to good outcomes". But I tend to steer players away from the torto shields because MSI is more valuable than bashing. I'd rather have Heater Shield than Omegaward. But this is a small matter of taste.
For armor you want sets that match up type damage and status resistances in order to get the most from them rather than having mediocre status and damage resists all around.
I agree about the statuses. For example, post #5 specifically recommends a fire-heavy armor setup. Damage protection is less important to me.

The thing about MSI is that it's the crux of some builds and the dump stat of others. I like to use it with bombs and guns that enable me to strafe and swords like winmillion and dread venom striker that have a lot of knockback and propel the user forwards, so that I can pick out an enemy (usually a gremlin bomber or mender) and kill just that one enemy. I'd much rather have the tortoshield charge if I'm using swords that don't propel me out of harms way, or if I'm just not planning on strafing so much and would rather build up defensive stats being HP.
So really I'd say that the OP should go for omegaward if their weapons benefit from it AND they're capable of using shield bash effectively. I'm guessing that the OP is incapable of shield bashing effectively enough to warrant getting omegaward, and should probably just stick to a normal shield or swiftstrike.
---
And silversaps are not a HUGE problem. They're one enemy out of like fifty that the player rarely encounters (not even in a major boss stratum) and can usually deal with by not running up and stupidly getting hit while trying to dish out nine million damage, being fancy. It's just that when the player does happen to get locked in to freeze at full HP it feels absolutely awful and unfair and it sticks with them that they'd BETTER get that heater shield with a stun max variant or else.
Instead of reading the Swordmaster Guide, try reading my detailed sword guide. It is...better. See the section on mixing weapon types.
Are you talking about one sword and one gun? I'll assume so for now. Here are some answers.
* Combuster with Blitz Needle. Combuster pretty much destroys anything that isn't gremlins, beasts, or Vanaduke. Beasts are too easy to worry about. Blitz destroys Vanaduke. And it's okay against gremlins. Charge time reduction helps.
* Nova Driver with Acheron. Acheron destroys anything that isn't fiends and undead. Unfortunately there are many of those in the later parts of the game, so you'll be using a whole lot of Nova Driver there. You want lots of charge time reduction. You must have auto-target off, and you must practice landing the ricochets. They are what make alchemers powerful.
Other powerful swords to consider are Warmaster Rocket Hammer and Final Flourish/Barbarous Thorn Blade. Other powerful guns to consider are Storm Driver, Umbra Driver, Grim Repeater, Iron Slug, and Callahan. The pulsars are also useful, when used well. And it's fun to try other swords and guns. And there are many interesting and powerful bombs too.