new to riding

Don't get a fixed-gear, no matter what else people tell you. I have nothing against fixies personally & Austin doesn't have hills like where I come from, but there are some hills here & you'll want gearing options to save your knees, not to mention your lungs since you're just getting started. Whether you buy new or used, good brands to look for are Trek & Raleigh. (I ride a Gary Fisher, but that's the same as Trek since Trek bought them out a while ago.)

You were right to stand your ground re bike shop salesmen. You do not need to spend $$thousands$$ to get a decent machine for commuting or whatever. If I were buying new, I'd go for something between $500 & $700. $800 at the most, no more than that. Don't get anything carbon-fiber; bikes with CF frames are just expensive and disposable. Go for aluminum allow or steel, if you can find it. If you're looking for something general-purpose then steel frames are great, but if your bike gets wet then you must dry it off as soon as you get home, no matter what kind of paint or coating it has.

Ride to live, live to ride, ride to drink...

Sounds like you want a road bike. Or a hybrid. No mountain bikes, unless you replace the knobby tires with smooth tires. Which is certainly an option, and it doesn't cost much.

Yes, you want brakes.

You could go with a fixed gear (one gear) bike as people here have suggested, but Austin has lots of hills, you might be happier with a bike with multiple gears. They're not as trendy, but they're more practical.

As for cheap, if you've got time, the Yellow Bike Project might be able to hook you up. They used to hook people up for free if you volunteered 12 or so hours, but they lost their space. They had a nice sale a few months ago when they lost the space -- too bad you missed that, lots of great deals.

Other options are craigslist or Frankenbike. Garage sales often find you excellent deals, though you'll have to check a lot of them before you find the right bike. Goodwill stores often have decent bikes too at great prices, but most of what they have are crap.

Department stores tend to not have very good bikes. You're better off getting a good quality used bike than something at Wal-Mart or Target. Magna and Huffy are not known as good brands!

Whatever bike you get, make sure it fits you, or can be adjusted to fit you. Your height seems to be about average, so finding a bike that fits shouldn't be difficult.

A few bike shops sell used bikes. The University Cyclery comes to mind. But it all depends on what they've got right now. If you get your used bike at a bike shop, it's likely to be better maintained and adjusted -- but you'll pay more.

Budget some money for some LED lights if you plan on riding at night.

You need a single to not only efficiently navigate Austin proper but to regain that euphoric childhood feeling of flight...with brakes yo! Oh and remember dearie...if it aint broke don't fix it...late!
oh yeah...Clown dog,East Side Peddle Pushers, and The Peddler are all great shops but there are many so look around. Austin is small enough to hit ten shops in one day...late!

you need a fixed gear with all the matching colors.
fixed gears are like butt holes, every one has one.