My other thought was to buy a "donor" RC Truck from eBay or a store like Target/Walmart. But the choices are so vast I'm not sure where to start off in that path.
This -is- the least expensive method - but you don't buy one off of ebay or at a store...
You buy one from Goodwill or some other thrift store. It typically won't have the transmitter, but you don't care about that. It shouldn't cost more than $10.00 USD ($5.00 USD is the norm, at least here in AZ). You can find them even cheaper during half-off Saturdays.
There is mainly one brand you are looking for - New Bright Toys. Once you find a suitable chassis, you'll want to inspect it to make sure the wheels are all round, that the gearing is still good, that it "sounds" like nothing is broken, and that the steering mechanism seems in good shape.
The majority of the New Bright Toy vehicles use a chipset called the "TX2/RX2" chipset. It is a very, very common and cheap chipset used for creating these el-cheapo RC toys. Many manufacturers have used the chipset and still do (the SMT version is popular today; the DIP thru-hole was more popular in the past). If you do things right, you can use the pinout of the chipset to figure out where and how to control the h-bridges that control the functions of the vehicle.
Want to know more? See this old mega-thread:http://arduino.cc/forum/index.php/topic,86883.0.html