I'm submitting a few RPs, though, but none of them have started. If another one takes off and I can't participate, I'll let you know. Keep me on the roster for now. 

I suggest avoiding card games. I did this in an RPG and it worked well, but it was one-on-one with NPCs. You'll have to send PMs to each person for what cards they have been dealt. It can be done, but you can easily make mistakes and it would slow everything down, since everyone would have to post in succession for the story to proceed.

A scavenger hunt sounds good, but draw a map on Paint or something ahead of time and post it so we know what the building looks like. You could set it up so that each player searches a specific location and you tell them if they found something or not, I guess. 

"I search lockers 1A to 5A."
"You find (blank) in 3A!"

But you'd have to set terms for how many things a player can search at once.

Paintball would be pretty epic too, but we'd need a lot of players. Hmm. You could add CTF as a mode. Much easier to keep track of score. Make sure you look up a list of paintball rules of engagement on a website somewhere. 
---
There's a good bit of work and research to be done here, it seems. I apologize for being the overly logical one but I put a lot of thought into anything like this ahead of time. "Make it up as you go" rarely lasts. Keep us informed! I haven't done a school-based RP in a while.