My suggestion is to talk to Wayne Cokeley from Team 25. They started a program called RINOS (Rookies in Need of Support) and this program & 25 will have a lot more information to offer you!
My team was started by a junior, his best friend, and his parents, so it is CERTAINLY possible for a student to be the major force behind it. Talk to EVERY teacher in the school, even an English teacher might be interested! Sometimes just a teacher and a few parents is all it takes, but even if you end up engineer-less, parents are a HUGE help! Each year my team holds 2-3 parent meetings to let them know what's going on and how they can get involved. If you'd like, I will gladly email you a copy of our parent handbook.
Our first year, we didn't even have a machine shop, so it is capable to do without one. My suggestion is to get whatever tools your parents/mentors/sponsors have, and use them! Never say no to something offered! Space has always been a struggle. Ask your school if they have an empty classroom or even some spare closet space. Field components generally DO take up a lot of space, but you don't necessarily need them. Try to find other teams in your area and see if you can use THEIR field parts, most teams are more than willing to lend it out, or at least offer its use at their own school.
Finally, fundraise like CRAZY. Car washes, and even little things tend to bring in a lot more cash than you expected. Also, try to get a nice letter and some general information (Brochures) about FIRST and your team to show possible sponsors. I know our rookie year some of our members went door-to-door looking for fundraising from all the major businesses in our area. I can also give you some of our generic fundraising stuff, if you'd like to use it for a model!
Let me know, and best of luck!
Sara "BandChick" Reffler