Buying and Registering

If it's going to remain parked on your property, and not pulled on the road once you get it to your lot, you may not need to register it with the Texas DMV at all. I assume Illinois, like most states, offers a temporary transit permit sort of registration which would suffice for getting it from there to Texas. (Whether it needs to be registered even if not driven mainly would depend on the zoning etc. restrictions of the locality, I think; some places forbid keeping unregistered vehicles out in the open in your driveway, etc.) Naturally, if you'll be pulling it some (maybe to dump the tanks or go camping), then it needs to be registered.

Intuitively, I agree that Texas would make the most sense; but occasionally the law does not agree with my intuition.