Go for it!!
FIRST is an excellent experience. With the amount of students and knowledge base you mentioned, FIRST will be a perfect place to develop your skills. The kit you will receive will have everything you need to make a basic robot. The default code for the controller is provided by FIRST and is fully functional as provided. FIRST does this to make it easy for rookie teams to get involved. However, with the background knowledge you already have on your teams you will be able to do so much more. If you want to try two speed transmissions, check out the white papers on this site and designs are provided for you. Or if you don't have access to the machines needed to make these components, order a gearbox from
AndyMark, they will give you all the torque and speed you need.
All you need to start a FIRST team is money, 1 adult, some interested students, and the will to learn. It sounds like you have everything you need already.
It's an amazing experience. If you have the opportunity, I would not pass it up. If you need any help, just ask. This site is an excellent place to start.
If you have any specific questions, or would like to see some video footage of last years competitions. PM me and I can show you where to find this.
Good luck!!