Good Q.

First of all. Like tanks and battleships we have the basic triad of power.

Manoeverability/Speed= drivetrain/control
Firepower= Weaponpower/armor defeating capabilitity.
Armor/survivability= Armor/redundancy
With a finit weight limit we have to balance these 3 according to the wish of the builder.

For control you have a Basic Radio Control system. 99% of the time RC stuff, like used for remote controlled cars/boats. Legal issue- you cant use dedicated RC plane 35MHz comercial setups for the robots.

Drive/power. Batteries and electrical Direct Current motors driving the wheels trough a reduction gearbox and controlled by Pulse Width Modulation speed controllers are the most used. You could try other means, but then I wish you good luck.

Weaponpower. A few mayor High power weapon groups. Axes, flippers and crushers.
Of course there are lower power versions of these, with Axes as the weakest of these, Flippers have the lifters as low power brother and the crushers have the grabbers/clampers weak version. Fast acting weapons can be directly powered by pneumatics, or very creatively , electrical. Slower weapons, if powerfull, mostly are hydraulical in nature and have proven devastating if done well.

Armor/redundancy. If the robot keeps on moving, in a controlable fashion, it can win the fight.