I've never actually built a robot (will need a garage first really), though I have thought about it, and have a bit of personal interest in it. But for the most part I'm talking out of my ass or something.
Chances are you'll want to use a standard R/C car/airplace/helicopter transmitter/receiver. The more things you want to control independently, the more channels you'll need, the more money you'll have to spend. Starting from $50 to $1000+.
To move the robot, if you want to build anything of substantial size you'll want to avoid standard hobby parts (like motors and batteries). Gas power would be cool. For electric power you may want to read up on the people that are hotrodding their electric razor type scooters. See what kind of batteries they're using, and what kind of motors. They're able to hit 20+ mph with a few miles range, with 180 lbs on the scooter. I think those should apply well for a robot, though in an R/C car world 30mph is nothing. But at the same point the cars are very light, and the motors have very little torque.
I used to get catalogs to
The Robot Store. They had a lot of interesting stuff, but I don't recall them have parts that would work for larger robots.
Oh yeah, and I was reading about one robot, they had a pneumatic ram. For the pneumatics, they went to a paintball shop and had them custom made.