The standard hotel taxes sometimes drop off after 30 days. This depends on the local municipality though. You can also generally get a better rate by calling.
[1] https://en.wikipedia.org/wiki/Category:Extended_stay_hotel_c...
Looks like lots available in DFW area if thats where you're headed.
https://dallas.craigslist.org/dal/sub/d/dallas-from-40-nt-21...
Bed bugs is a tricky one, maybe look into some traps, toss the sheets when you get into the room and look for blood spots(I'm sure there are travel blogs with more advice on this).
Wifi is probably decent most places, Texas is a populous state so there has been quite a lot of investment in connectivity.
As far as AC goes, Texas is warm but I was there in May a couple years back and needed to put on a sweater so I wouldn't make that a priority considering summer is almost over.
You could always get a hotel for the first week, then view a few places once you get to your town, this will allow you to check out the neighborhoods and find one that fits your lifestyle.
If you're moving to the DFW, they have a really good transit system with rail connecting the three major cities. I believe it was called DART or Dallas Area Rapid Transit.
Good luck!