How to buy a used car in Texas if you are a newbie?

hello, you don't actually need to have a Texas driver license to buy a car but you will have to get it eventually.  Yes, an international driver license will be convenient at one point but normally you have up to 90 days to use your home driver license before you have to switch. you will need a car insurance though.
You will need to have a social security number (SSN) which you obtain with proof of legal residence in US (which is a work visa usually).  The car plates don't change unless the car is at least 5-6 years old and then it's kind of a requirement but htat's usually included in the price you pay for the title change.
Buying a car is not difficult, there is plenty of choices, most car dealers here will take in a used car as a trade for a new one someone wants to buy, so they all have used cars for sale.  Otherwise, the newspapers, craigslist.  If you buy directly from a individual, check the title to make sure the owner has plain rights, if from a dealer, that should be typical.  From an individual you don't pay sales tax, from a car dealer you will.  Dependent on the type of car, it can be somewhat expensive.   
Yes you will have to change the title to your name, the cost is a percentage of the sales price.  It's not that expensive.
Car insurance can be had at a very reasonable price, and sometimes the car dealer will provide you with favorable contacts.
About $100 a month is somewhat correct, for someone who has never driven in the States, you start with a blank state and therefore can be considered a risk.  There are companies like AIC and TravelGuard that offer memberships in order to bring expats some good deals on certain types of services.  Car insurance is one of them.  Car insurance price can be lowered but the membership cost for the year (not too expensive) can offset the savings.