The Texas Department of Transportation says you can keep your plates (but it's not clear that you have to).
You should be doing a bill of sale along with filling out the back of the title (or whatever Texas requires). Those documents should be enough for the buyer to show to a cop that the car was just purchased (so long as not much time passes between the sale and the vehicle registration).
Texas DOT used to have some online forms, including a bill of sale I think. It's one of the worse DMV web sites I've seen though - good luck finding it.
If you are selling to a dealer, there's something in the rules about the dealer having to remove the registration stickers and some dealers may be reluctant to give you the plates back.