If you have no technic and no power functions you will need to get quite a lot. You could buy small technic sets to get enough parts to build the moving parts and you your current collection, or buy a big set and just add power functions to it. The Customized Pickup Truck is a good starter set that has all the right moving parts, but pretty much any Technic truck/car contains steering and a drive chain that you can attach a motor to.
For steering I recommend the servo motor. As a kid I spent a lot of time making cars that would lock left or right but not flick back to exactly straight afterwards.
For propulsion you have a whole array of motor options, the biggest and strongest (but also the slowest) is the XL motor. I've seen the Customized Pickup Truck converted to full RC using two M motors.
One IR receiver can control two wires so if you're only thinking about propulsion and steering one will do.
You'll need a battery pack. I prefer there one that takes AAs because years from now AA battery will still be purchasable and may be even longer lasting, plus you can keep spares near by, as opposed to the Lego rechargeable battery which will wear out over time and not be available forever.
And finally a remote. The speed remote lets you control the speed of the motors, not just forward/backwards at a fixed speed. However you'll need some extra parts to make left/right steering make sense on there. The other option is the basic IR remote. Either one can control two functions.