My basic situation is that I need to remotely control my tank style robot. What are my options for doing this?
Radio waves of some sort. Which frequency and which technology depend a lot on what kind of data you are trying to send and receive, and what your speed and reliability requirements are.
IR requires line of sight, and some means of keeping ambient light from interfering - something that is difficult to manage if you are thinking about operating outdoors.
RF receivers and transmitters come in a lot of styles, frequencies, prices, reliability. The more reliable, longer range, higher data rates, the more you can expect to pay.
Blue tooth is limited in range, and success stories are pretty scarce on this forum.
Wireless game controllers are generally pretty limited in range and in the kinds of data that can be sent, and require a matching receiver.
Any and all suggestions are helpful (except for setups the would cost upwards of $50 US
$50 barely covers any kind of reliable communication system with any range and transmission rate.
Of course, what will work depends on a lot of things you haven't stated.