You might be able to join a credit union and get your US banking done that way (we did).
Will your wife's employer arrange health insurance?
We kept our UK house on and rented it out - we needed permission from the mortgage company to be able to do that though. Just used our UK bank account as normal (and with online banking now this will be straightforward).
Houston is huge - which areas are you looking at? We chose an area with a straightforward commute from home to office but even then it could be really slow. A good realtor to help you find houses for rent / purchase are worth their weight in gold. Are you already browsing HAR.com?
If you're shipping across furniture then it pays to rent a furnished apartment for a few weeks, which also gives you a chance to find your way around and look for a good rental. It took around 4 weeks for our furniture to arrive.
We were recommended an insurance agent who took care of things like home insurance, car insurance etc. We bought our first car from CarMax, and used their buy back option when we left.
You'll have 30 days to start the process to take a Texas driving test. We did ours in Richmond or Rosenberg (can't remember which) as it was rumoured to be an easy test centre.
As a non-working spouse I didn't have a social security number, but was given a tax identification number (TIN). I found that there were lots of things I couldn't do (like get a mobile phone contract) without an SSN, but that was a few years ago now so that might have changed?
Also second paying someone to do your tax returns!
Arriving in summer it will be hot and humid, and I'd avoid anywhere with bayous (but I was a magnet for mozzies). Be aware that your summer electric bills will be high running the A/C (we had friends that had two storey houses but they just lived downstairs in the summer to cut down on trying to cool the second storey).
We bought our electricals at East - West in Houston, as they do dual voltage stuff which gives you the option to bring it home (we bought a dual voltage TV). Think we also got a cash deal for buying fridge/freezer, washer, dryer and TV from them in one go.
One thing I was unaware of was venomous spiders (black widows and brown recluses - not that I ever saw any of them) and snakes.
But there's loads to do out there - local state parks, Galveston, Corpus Christi, NASA at Clearlake, Austin and San Antonio for weekends away, the wildflowers in the Hill Country.