[Lil' Lavery]

Another option may be the FIRST Vex Challenge. It serves as an amazing low-cost alternative for FRC. It could be in conjunction with FRC, instead of FRC, or as a stepping-stone to FRC during your HS's first couple years of involvement with FIRST, or a number of other things. All you really NEED to build an FVC bot is a programming kit and a vex starter kit, but I would recommend getting more. The total part cost for a typical FVC bot runs around $500-750, including the programming kit. Likewise, the only tools you NEED are the two allen wrenches and the one hex wrench supplied in the starter kit, but I would reccomend a dremmel, vice or other clamp, hack saw, loc-tite, lots more allen wrenches, file and wire cutters for more intricate work. But the total cost of FVC tools is typically no more than $100-200 dollars, even with replacements and extra tools. An FVC team only nees 4-10 students, and preferably 1-3 adults to help with administrative duties (like travel). The travel costs are less than an FRC team (don't need as many hotel rooms, a full bus, etc.), but still not incredibly cheap (depending on the length of travel to the desired competition). Team registration is also cheapER, but still not cheap. I'd reccomend trying to find at least one sponsor to help with costs.

As for FRC. Yes, it is possible for a High School student to be the catalyst behind the creation of a team, but you need support. FRC Teams typically recquire a minimum of 10-15 students, but it can be done with less. I't is also incredibly helpful to have at least one adult mentor with mechanical/engineering expierience and one with programming expierience to help guide the students. It also helps to have a school faculty member to act as a school sponsor and help coordinate activities with the school.
Work space can be a team member's garage or basement, a classroom, wood/metal/autoshop, warehouse, barn, or many other locations. The only NEEDED tools are a drill, wire cutters/strippers, hack saw, phillips, allen, and flat-head screwdrivers, clamp/vice, SAFETY GOGGLES , hammer, file, and tape measurer. Dremmels, soldering iron, bench tools (drill press, grinder, sander, band saw, etc.), arbor press, calipers, mill, lathe, etc. are all very useful, but you can live without them. All of these tools (with the exception of the mill and lathe) are available at Home Depot/Lowes or other hardware/home improvement store, and it is highly likely that a team member and/or parent will have access to them.
Materials can be a simple/cheap as wood and pvc (along with the Kit of Parts supplied to all registered teams). Bots range from "boxes on wheels" to the beautiful and intricate wonders of aluminum, plastics, CNC machining and welding.
The field isn't essential to build, but I highly reccomend building at least the scoring attributes (goals, scoring objects, etc) and any element incorporated in your autonomous programming (such as the light or Infra-red of previous years games). Teams can often share fields if they are nearby.