Where are you based? Antweights and beetleweights are the best scale to build to for club events on a limited budget as it's fairly easy to build a makeshift arena (unless you build spinning weapons). Outside of the club, antweight and beetleweight arenas/events are most popular in mid to southern England, antweights having their own events and the beetleweight arena being at most heavyweight events run by event organiser Robots Live.

As Niels said, the budget it quite low. You'd only get maybe a few ants out of it, a beetle or two and very little in the way of a feather. The transmitter/receiver costs are better than they used to be but the £40 Niels mentioned is for one of the more basic models so two of these would use up over half your budget. Could perhaps be an idea to encourage the students to buy their own RC gear (which they can always transfer over to another robot if they decide to branch out) and that would free up more budget for parts. A website called Technobots sells small continuous rotation servos for about £6 that are ideal for a basic antweight drive. They don't need an external speed controller to control them as it's an all-in-one unit, so you'd just need a battery, add in the receiver, an additional normal servo (for a basic weapon) and throw it all into a chassis to get a few ants on the go.