Yes, I can guess this comes up a lot.
I have a 3* cobalt set (all at level 10), and am getting a brute jelly set (helm: 10, mail: 1, shield: not yet). I'm guessing brute jelly is better because of the pierce defense. I prefer a sword, and the choice is between Calibur, Nightblade, Fireburst, and Sealed Sword (all 3*). I'm comfortable with a 3-swing combo, but lots of people say sealed sword is better, so it's between that and Nightblade. I end up using a gun a lot, but I have only one 3* (firotech) so no problem with that. (I have only two slots), or should I get a shadowtech mk II?
While wolver line armor would be better since it has sword damage bonuses, cobalt will work pretty well for now. I actually sometimes use an elemental resist helm or armor with a pierce since I usually have more trouble with gun puppies and lumbers in close quarters, and JK himself and the minis don't deal piercing damage.
As for swords.... calibur will not give you any extra damage against any enemies, but the charge attack is very useful for gun puppies, lumbers, JK (he will get hit 3 times if you aim it right), and for knocking back monsters in halls or tight places.
The fireburst will get you extra damage against lumbers and gun puppies, and the charge attack is great for keeping JK hurting.
Nightblade is probably your best bet, since you do fight slimes mostly, and you are going to be using a sword for your main dps.
I haven't used the sealed much, but it has only normal damage and is very slow, so without armor or trinkets for asi it's probably not going to work well, except for its knockback.
I would suggest going with nightblade, and later get a sealed for making into an Avenger, since the Faust line really requires curse resistance to make the best use of it, so you have elemental and shadow weapons.
As for a gun, a firotech is about perfect, IMHO. It's really the construct stuff (lumbers and puppies) that you would want to use a gun on, and it is strong versus constructs. Also, the fire is useful for keeping JK losing health even when you can't hit him for a bit and for menders in the first 2 levels. I usually carry a nightblade (a 4* one now), a prismatech mk, and a fiery vaporizer mk, so you get the elemental plus fire with one weapon with that loadout.