How much heat will I need and how should I get it?

You haven't given us enough information. If the box is insulated well enough any amount of heat will be OK. If you want it to heat up fast, 50-100W should do it. You should look into PID control to avoid overshoot since you don't have any way to cool the box.

You could probably get a few crock-pots from a thrift shop and scrounge the elements from those.