Hope your move goes well! I live in South Texas, so can't give specifics, but as a I've been a homeowner and a renter and worked in real estate and renting has been a nightmare, so I can give you an earful!
Distinguish between renting directly from an owner versus a property management company. Make sure you read contracts carefully because many of these companies have all kinds of nit picky little things like they charge a fee on repairs, etc.
Visit the neighborhood! This is SOOOOO important, drive through it at all times of the day, morning, mid-day, night. I wish I would have done that with our house becuase what is seemingly a quiet and nice neighborhood has all kinds of riff raff drive through it and kids from the elementary school walk through people's yards and throw trash and quite frankly, the people are unfriendly. So...be really picky and check it out from all angles and perspectives.
Check the house for major issues really well. 2 months after we moved in to ours, we found black mold behind a loose shower tile and major water damage! Be demanding! Stand your ground on having proper repairs done and done timely. Be sure you know what your responsibilities are in terms of yard care, whether there is an HOA and who pays the fee and whether or not you can use the facilities and whether or not the owner or manager makes unannounced visits, etc.
Just look at everything with a magnifying glass and remember that usually homes that are used for rentals, unfortunately are beaten up and you will be limited to what improvements and changes you can make or request.
Best wishes, cross country moves are crazy, I've done it 3 times!!! Fort Worth is a great city and there's so much to see and do in and around.