I'm in that range, bought a house in Far East Austin for 158k. It's 13 years old in a divers neighborhood, the previous owner maintained it very well and it's a 3 br 2 ba. I got a FHA loan with 3.5% down, qualified for down payment assistance and mortgage credit certificate. Got 5% of the closing price from the state as a grant, doesn't have to be paid back for the life of the loan. Used some of it to pay for the down payment and the rest for closing costs. Ended up paying about 3k out of pocket after everything was said and done. The housing market is nuts in this price range. I got beat out by cash offers on 5 houses before this offer was accepted.

You really have to make some decisions, do I need the space a house can provide? Do I want a relatively new house that's far away from everything, or a falling apart house that's not as far away from everything but still kinda far? Do I want to pay for a house that in any other market in Texas would be considered over priced but is normal for today's market in Austin? What if that changes and I'm stuck with an over priced house? And do I want to deal with maintenance? In the first 3 months, I had to replace my AC's coils on the inside unit (used my home warranty and only had to pay 450 out of pocket) had to replace a part of my back yard fence because it got blown down in that wind storm a while back, and I still need to fix my smoke alarms.

It's possible to buy a house in your income range but I have to make decisions on if you want to.