In order for a tattoo parlor to be open in Texas, they
must be licensed by the Dept. of State Health Services. So as long as the parlor you're going to isn't in the back of some dude's garage, you should be alright. Just ask to see their license and inspection certificates. (They must be readily visible.) Texas is one of the few states that you can still donate blood after having gotten a tattoo there. In most other states, you have to wait a year.
A good way to learn about the local artists is to hit up a tattoo convention. Walk around, meet people, ask to see their tattoos. If you see one you like, ask who did their work. Or you can just head to the parlor and ask if the artists on the clock have portfolios you can check out. If they don't, skip 'em. They're either new or their hacks. Most will have an album at the counter. Also ask to see any original work, not stuff straight off the wall. If you like what you see, show them what you're interested in and ask them to draw something up. They should want a deposit of some kind. (Nothing's free.)
As to the cost, it depends on the artist and the size and complexity of the tattoo. Smaller, simpler tattoos will probably just be a straight fee, (45/a letter, etc.). Bigger, more colorful tattoos will be done on an hourly fee, up to 500/hr in my experience. If its more than 10-12 hours of work, they should cut you a deal. And tip 'em. The guy/lady is permanently scarring your body; you want them happy.
I recommend Sundays. They're usually slower days in the parlor and it won't ruin your weekend by making you have to tend to a fresh tattoo Friday and Saturday night. Keep the bastard moist and juicy afterwards, I like Aquaphor, but any A&D ointment should be fine.