I have a small single-family home (1000 sq ft), and it's in one of the areas mentioned :) Since you have so many options, I can see why it might feel overwhelming, but I don't think you can go wrong with any of them. The most important thing is that the numbers work. I'd look at the pricing on one of the sites and then correlate that with your purchase price. It's not like a regular rental, so you will need to have days for cleaning/turnover unless you can afford a service to do it in a couple of hours.
The type of home you get will just determine what type of client you'll attract. 1-bedroom condo might attract more business clients traveling solo (some of which stay for weeks and have an expense account), 2-bedroom might get more families on a budget, SFH might get more families more willing to spend. Because there is so much competition your prices need to be competitive, so I wouldn't go for anything too expensive on the far north/northwest side of town (personal opinion). I knew someone who tried to do it in a solid B neighborhood just north of Sea World and was losing money like crazy, so don't go too far out of the city center if you can. I know people with SFH that are doing amazing, and I also know someone with a condo near a gun range who is overflowing with bookings because of the specialized certifications they train for. Anywhere near downtown or around Fort Sam Houston or Lackland should also do well.
I can't speak to the NE side, but I think that might be decent as well. Home prices are still reasonable, and it might attract people who think Austin is so much cooler than SA and want to visit both cities.