Remember cheap used bikes usually need an overhaul. See if there is a bike maintenance course in your area to learn how to do your own repairs.
1: What should I look for in a helmet?
How easy is it to adjust the straps. If the straps are not just right the helmet is useless.
2: What should I look for in a first aid kit?
I don't have one.
3: What should I look for in a light?
I use a Maglite 3W LED held to my handlebar with hose clamps
4: Are there any other safety things I should look into?
read "effective cycling" by Forester
5: What should I look for in a lock? (Kinda have the basic idea here, would like more opinions though)
see sheldonbrown.com for answers to all questions.
6: Does handle bar type matter? I usually have problems with vertical bars, but normal horizontal ones are fine
7: Any other important things I should know?
2000 Montague CX, I do not recommend it, but still ride it.
Strida 3, I recommend it for rides < 10mi wo steep hills.
2006 Rowbike 720 Sport, I recommend it as an exercise bike.
1996 Birdy, Recommend.
Wieleder CARiBIKE (folding), decent frame.