As part of the Ruckus competition we have run Vex type competitions in the past, I will see if I can find some of our documents (Alex Cormier put together the last few).
Some suggestions if you want to run a small competition like this...
1. Stick with a kit that already exists for the electronics/motors... it will make things easier and more consistent across the teams.
2. Put a limit on the additional parts... like vex or FTC or any other similar competition either make a short list of materials that can be used, or even just use the rules from an existing kit/competition.
3. Come up with some SIMPLE rules & a simple field. The more complex you make the rules, the harder it will be, and the harder it will be for teams to participate/build their own structures.
4. You need to give teams a longer headstart than an FRC buildseason, especially if you don't have preestablished teams. Try to give teams at least 3 months to build their robots, if not more.
5. START EARLY... recruit teams, get their ideas, see what THEY would like to do, especially your first year. We've had limited success when we don't provide the game info early enough or dont advertise early enough.
6. Avoid key times. If you are planning a Vex based competition, it may be wise to avoid the Vex season. If you are planning to recruit FRC teams, avoid the FRC build season. If you want to get Lego teams, avoid their build season. Make sure you plan around major school events & holidays & factor them into team schedules (finals weeks are hard for kids, Dec-Jan is often tough, start of school often means vacations the weeks before, etc).
And lastly, my personal opinion is that battlebots is tough, especially in the FIRST community... we are so used to being able to use our robots over and over, being able to demonstrate them, that any competition that destroys 3 months of hard work is often a harder sell. Its a great spectator sport, but a very expensive investment (especially when someone chops up your vex or FTC controller module!!). But again, that part is just my personal opinion
Good luck!