The Night Hawkin is great. It's accurate and fast, and has extremely high damage for an elemental gun. Usually elemental guns trade off the bonus elemental damage with reduced regular damage, but the Night Hawkin doesn't, or at least doesn't do so as much. Also, keep your eye out for the following: Hellshock, Lob, and anything with the word 'Call' at the end of it. They're amazing on any character once you figure out how they're used.
And for shields, I always, always look for a Transformer. They're, in my opinion, the best shields in the game.
For FL4K, I found that the AI for the beast wasn't up to having them fight effectively unless you put all sorts of points into skills that boosted them. So I went with the Jabber, which keeps the pet at range and provides a little bit of added damage and distraction. When something tough comes along I'll use the attack command (he switches to rockets), but mostly I just ignore him. The one skill I did take is the one that gives him the ability to revive me in combat. Since he's ranged he's usually alive and near me, so it has saved my ass countless times.
I've played Moze both ways. I had one build that was all about high elemental damage and all the points were there to make Moze a badass. Iron Bear was just there as an escape if things got hairy. My last build, on the other hand, gave Iron Bear a very short cooldown and a very long uptime, boosted his damage way, way up, and made him really tough. The trade-off was that Moze was fairly weak, damage-wise, when on foot.
One symetry trick to look at with Moze, almost any build:
~Transformer shield (high capacity, shock damage restores shields instead of damaging you)
~Deathless relic (Reduces character health to 1. Increases shield capacity by 100%. Increases shield recharge rate by 25%, decreases recharge delay by 25%. )
[These two alone give you a shield+health pool that is much larger than it would be with a regular shield and lots of health. Significantly larger.]
And the following skills:
~Armored Infantry (gives increased damage and personal damage reduction when your shields are active - which is 100% of the time.)
~Thin Red Line (reduces your max health by 60%, increases your shields by 60 %. As your health is already locked at 1, the downside is neutralized, and this is just a 60% shield increase on top of the 100% from the Deathless relic)
~Vladoff Ingenuity (+30% shield)
~Desperate Measures (increases your gun damage based on how low your health is. Note: Your health is locked at 1, giving you a constant 50% damage increase across the board!)
So, short version: You have constant 13% damage reduction, +65% gun damage. You have 1 health, but +190% shield capacity (you can take probably twice as much damage as max health + regular shield), extra fast recharge, and shock heals you.
Shock heals you means that anything that does shock damage. That means that shock enemies can't hurt you. It means that damaging a shock barrel and standing next to it makes you invulnerable. It means that guns like Kill-o-Wisp or a shock Devil's Foursome become instant healing. Just shoot the ground until you're full again.