Welcome to Texas! I hope you will be really happy here. Houston isn't pretty (although it has beautiful spots) and the weather and traffic can be tough to take, but it's a lively, diverse city and the people are great. Happiness in Houston is about keeping your commute under control, so I would start with finding housing near work and since you are coming from overseas, just plan to rent somewhere for a year until you figure out the traffic patterns. (Travel time is about traffic, not distance, and it's not always intuitive where the snarls tend to be.) The good news is that a huge number of new apartment buildings are opening all over town, which is finally making rents more reasonable after several years when there was not enough rental housing for the influx of new residents coming in, with accompanying ridiculous rent prices. However, unless you are both living and working inside the loop, you may need two cars as Houston is not super bike/transit friendly.
In terms of move-in costs, you will need at least first month's rent plus deposit. Internet and power would likely need deposits, although if you're in a rental the landlord will probably be paying sewer and water so you don't need to worry about those. There will be a fee for your Texas driver's licenses (registration for the car(s) would be included with purchase). You will definitely need car insurance and you probably should have renter's insurance...check the flood maps and talk to your neighbors, and if you are in a flood zone, buy flood insurance too. Be careful about a first-floor unit, particularly if you're anywhere near a bayou. It's not just hurricanes...down here we get a lot of short, heavy thunderstorms that dump water faster than the drainage can carry it away, and either it backs up onto the streets (and into cars, be careful where you park) or overflows the bayous as the water moves downstream.
Possibly fees associated with cell phones depending on how you are setting those up. Since you're coming from overseas and I assume won't be bringing a lot in the way of furnishings, a big variable would be how you plan to acquire those. We do have an IKEA and a variety of local second-hand thrift shops and on-line lists. If you want to do the "slow furnishing" thing with shopping gradually for used items, the mini-van might actually be a good idea. If you're buying used cars, you might want to think about a AAA membership. I got mine a couple of years ago and it has totally been worth it since I drive an older car.