The problem is what you are budgeting for truck and camper is typically what you pay each for a quality unit that didn't require fixing. You need to expect that there will be maintenance and repair required on $10k units, yet you said you had enough.
Depending the camper you find, a 250/2500 class truck may not have enough capacity since you plan on full timing in it. Getting a large enough truck that is reliable for $10k is not easy and most likely will not be diesel. Since this truck will be big to handle the camper, it will not be a city car that is easily parallel parked or fit into all parking garages. Regardless of truck chosen you will need buy tie downs, turnbuckles and possibly wiring harness, tires and suspension aids. This cuts even more into your truck or camper budget.
As I stated previously, you are choosing an expensive RV option on a very small budget.
