If you do end up needing proper radio gear, then one of the best sites is probably http://www.sussex-model-centre.co.ukhttp://www.sussex-model-centre.co.uk they have great range of gear for all price ranges.

Radio car stuff is OK if you want to make a robot that wont take part in serious competitions (as it appears you are planning), however for legal robots that can actually fight in the competitions, R/C stuff from radio control cars can be more trouble than its worth.