Selecting a radio control for the most part is very easy. The main thing you have to consider is how many channels you need. By this I mean for each motor that does its own function that motor will need it own independent channel on your receiver. So if you have a motor that operates a spinning weapon and two motors that drive the robot, where the drive motors operate separately so that you turn using the tank drive option then you would need a 3 channel receiver.
Now I don't want you to get confused and think that the number of motors decides the number of channels that you need. For example, if you have a set of motors operating a spinning weapon, you only need one channel for those motors. You will just have to splice together a receiver wires so that you can plug it into one channel.
The next thing that you will need to consider is the frequency range that the controller operates. To decide this you need to look at what the competition allows. The reason for this is because they want to be able to jam those frequencies if they need to for safety reasons. Also, for some controls you need to assign a matching frequency to the control and the receiver. Others, like the Spektrum controllers, sync with their receiver and will only talk to that receiver after they have been synced. If you have controller where you need to assign the frequency to them, you need to let the people who run the competition know, so they can give you a frequency that will not interfere with anybody else's controller.
Finally, one other thing that should be considered is how you are going to power your receiver. Typically receivers operate at a much lower voltage then your motors will. Due to this fact you can't connect them to the same battery that your motors would be connected to. This means it will have to go on its own circuit, and since it has to go on its own circuit it will have to have its own off and on switch, for safety reasons.
Below I show a list of Spektrum controllers with there price on Amazon. I personally recommend these controllers, since they are easy to setup with very little programming involved.