Is there anything other than hull improvements in the Armor branch? I've been seriously neglecting it because I don't care a whole lot about hull, and I just want to make sure I'm not missing out on some cool planet structures.

I'm on 120 hp hull per plate so I guess it's all about hull in that tree based on the pattern that I saw so far..

Planet structures are only in the following research branch
Weapons (att structure)
Shields (def structure)
Stealth (cloak structure)
Planetary structures (pop/production structure)

This isnt entirely related but would you rather pay to repair hull or wait for shields to recharge? I cant decide whether I should go shield research or hull.

Hull if can handle/keep up with the costs and shields if your rarely attacked/attacking.

Actually, shield is best used as buffer and regeneration ability while offline while hull is best used during online.. Also, shield is good extension to the hull if you got 5 hull plates maxed out..

IF you are trying to withstand 400 damage from missions, I would choose shields (shield restore after getting hit 400) or hull (assuming that you cant hit 400 shields)
If people attacks your randomly, shields will be a better choice as it regenerates. If you are in war and constantly repair, hull will be better as it gives more 'HP' per size when compared to shields. But take note that having too much "HP" without sufficient defense is bad.