Not a rigger and I've only got 55 jumps, but having just gone through this process I think I can offer some help. Feel free to correct more-wizened-jumpers.
Open of full face is completely user-choice. I assume you've been jumping with an open-face during AFF, see if you can borrow or try a full-face. In general they reduce noise and wind smashing against your face. Some people dislike that aspect of skydiving and go for the full-face, others love it and stick with open. It's up to you.
As for jumpsuits, there are two primary types that you'll see most often around DZs - freefly suits and RW (relative work) suits.
RW suits are likely what you've been wearing during training. They have grippers (handles) on the arms and legs that are used for grabbing and making formations during skydives. They're designed for flying on your belly and doing things with other skydivers who are doing things on their belly.
Freefly suits are designed for freeflying (makes sense). They typically fit looser/baggier than RW suits and lack the grippers.
Other suits out their include wingsuits, tracking suits, and other variations (freefly pants, etc etc).
Most peoples' first jumpsuit is an RW suit. All of the recent A-licenses at my dropzone got RW suits (and coincidentally we all got Bev Suits).
Before you pull the trigger on ANYTHING, talk to the people at your DZ. I chatted with well over a dozen people asking about different suits, helmets, altimeters, etc. I had people show me the different suits, examples of different materials and gripper sizes, etc etc. Use the internet for cursory research, but there's nothing quite like seeing the real thing and getting advice from people in real life.