Here is how we handled it. Two months before selling the house we signed up for our mail service, St. Brendan's Isle in FL.
Then we we started the process of changing our address for our utilities, bank with new checks, insurance statements, and everything else. You will need some of these documents with the new address later. Do not change your address with the post office yet. While waiting to make to official move we simply had the mail service periodically send our mail back to our house.
When we sold the house we then notified to post office but by then most of our mail was already going to the mail service. Next step for us was to go to Florida and register to vote, get drivers license and register our vehicles. Took about three hours including a lunch break. Here is where you will need "proof" of residency. They will want some official documents with your new address on them, the may be utility bills, insurance documents, bank statements, etc. Even though our utility was Indianapolis Power and Light it had the Florida address and so was acceptable. If you go to the mail service web site they will most likely have a detailed description of what you need as TX might be slightly different.
Remember you will need to change things like Last Will and Testament, medical authorizations and such as these are only recognized if they are from your official domicile state. Your medical insurance will most likely change as well.
All in all its a pretty simple processes long as you have the necessary documents.