First Time Buying Used Car in Houston

Just arrived in Houston 2 weeks ago, and I'm looking for some advice on what to look out for when buying a used car here, and if anyone knows of a mechanic or mechanic's shop where I can bring the vehicle for an inspection before I purchase it this weekend.

I'm only here for a few months but renting a car for those few months would work out to more than just buying, registering and reselling a car afterwards. Found a car on FB for $1000 so hoping it goes well.

Also, how does the transfer of title/license plate system works here? From what I understand I would need to prepare the following before I meet with the buyer if I want to legally drive it away once the seller removes their plates from the car.

1. Proof of insurance BEFORE I buy the car (Any recommendations here for the cheapest insurance? I know minimum is bad but at current prices I've checked for $250/month I'm going to pay more for insurance than what the car is worth. No prior car purchase/insurance history in the US is the culprit i assume)
2. 30 day temporary permit from the DPS (Application for Timed Temporary Permits (Form VTR-66))
3. I know that I should also check for any existing liens on the vehicle before I pass the cash over as well so I think that's covered.

And I would need the following when I drive away to apply for the transfer of ownership:

1. Bill of sale
2. Blue title

Anything else I'm missing or any recommendations? Thanks in advance