Using a remote control for an EV3 robot?
You can't start a program with the remote (8885) or beacon (45508), however you can certainly have your program respond to a remote or beacon if you have the IR sensor (45509). So what you desire can for example be achieved by embedding your base program in one big loop and at the start of the loop have the program wait for a button pressed on the remote or beacon.

Unfortunately the education version does not contain the IR sensor (it is distributed with the commercial version 31313) so you will have to buy that one separately as well...