Autoguns are the best guns for staying still and pumping out damage:
Needle Shot -> Blitz Needle
Dark Chaigun -> Grim Repeater

If you're running with few weapon slots, the I'd recommend the Magnus -> Iron Slug. Iron Slug charge shots will work in almost every combat situation.

Blitz Needle is famously overpowered and the most popular weapon for taking down Vanaduke.

Storm Driver offers very good damage and useful status. It takes a little while to master the ricochets, but they are the key to alchemers, because they basically double your damage output. Here is a short explanation.

Winter Grave is good, although not as good as Callahan. The freeze often interrupts the charge attack, so that monsters don't ride the full charge attack for full damage. (The same problem happens with Glacius.) But freezing monsters can be useful too. So go for it.

What helmet and armor would be nice for these charge oriented weapons?

Well, you want handgun CTR, so that suggests Chaos, Seerus, and maybe Padded. By the way, you also want damage bonus and ASI. In particular, ASI can help you recover quickly from attacks. For a complete list of your options, consult the gunner section of my armor guide.

Would I be better off getting grim repeater, storm driver, and callahan then?

That is also a good plan. However, Vanaduke is disproportionately important, and Blitz is probably better than Callahan against him. So your original plan is slightly better than this new plan.

Also, which 3 star version of these weapons would I get first, and which one would I upgrade to 4 star and 5 star first respectively?

Keep in mind that you actually need just two of these weapons. So maybe you should take two of them to 5 stars, and then start the third one. Which one you leave for last probably doesn't matter much. If I must pick one, I'll pick Winter Grave, because the end-game monsters disproportionately resist shadow.

Blasters and Pulsars are good guns with knockback, aim right and you may need to move very little.

Fiery Pepperbox, Grim Repeater, Iron Slug, Callahan, Winter Grave are all guns with great knockback on the charge. If you have a high enough CTR you can sit in the back and fire a charge shot to push enemies away.

I would still promote learning good movement patterns in the game. There are several situations in which you are forced to move while fighting. In fact before every battle try to map out your possible paths and then try to keep monsters off you by following that path. Playing by yourself makes controlling monsters easy, since they all go after you, you can lead them around the room while firing as you keep backing away.

Winter grave + callahan would be decent, but only with CTR.

I wod recommend Blitz Needle + Winter Grave to cover all of your damage types most efficiently. You wouldnt need elemental, since blitz can take care of undead and shadow weapons handle constructa sufficiently. Mecha knights will be your biggest challenge, especially in arenas, but a few winter grave charges should keep you clear.

The distribution of damage in the magnus-style charge attack is a little tricky. Most of the damage seems to come at the end of the attack. You would rather inflict the second half of the attack than the first half. For some enemies this doesn't matter; they ride the whole attack and die. But for other enemies it seems to make a difference. Maybe someone else can give you more specifics.

In case you don't know, the most important thing about the magnus-style charge attack is the knockback. Monsters don't get knocked in the direction of your bullet, as with other weapons. Instead they get knocked in the direction of their backs. So, if you want a monster to ride the charge attack for full damage, you have to shoot its front.

The only one I can think of is polyps. The bigger issue with them is that they are stationary and cannot be knocked back at all. You have to experiment, to see how they take a magnus charge. I don't have an explanation off the top of my head.

For example, lichens may not look like they have a front, but you can tell where their "front" is when they move in that direction.

The front of a monster is generally which direction it is moving. If something like a Lichen or Jelly cube is moving towards you it's "front" is facing you.

Don't ditch the magnus yet.... the regular shot is quick enough to catch those pierce weak monsters and has a high enough flinch chance you can usually flinch them in just one shot. In addition to this most of the endgame monsters are undead and fiend and your Tundrus won't be much use there.

Learn how to switch shoot guns and you can find some nice combos with the 2 clip guns. Alchemers for dual status (fire and shock), Magnus(or tundrus)/Autogun to lock them with flinch and easy DPS with the autogun (Tundrus/Darkchaingun and Callahan/Blitz).

The Needle shot works great for either eliminating single targets with the charge attack or by giving spread long range damage with the charge. It pairs with the Magnus gun because the Magnus can temporarily immobilize targets for the Needle shot.

Pulsars are Ok weapons but it can disrupt teammates. To use one correctly you must learn how to spread and time your shots in a way that herds the enemy to one area of the room. Once you get them there your team has more free space to operate. One of the best Pulsars in my opinion is the Flaming Pulsar line. While it's status has no effect in the Final boss the level the Elemental damage paired with the fact it doesn't get a status that inhibits knockback means you get nice power and control.

Chaos is a powerful armor but if you can't dodge you'll end up very dead.