I'm not familiar with the San Antonio market, can only speak to the Raleigh/Triangle area market but here's my take:
1) I'm currently invested in Raleigh, Cary, Smithfield, Selma, and Lake Lure NC
2) I would consider other cities in NC, but not in TX just due to proximity.
2) SFH vs multi... there are a lot of factors, so depends on how you define "less headache". Speaking in generalizations as it really depends on the deal, but SFHs won't have as much cash flow as a multi typically. You may have more options on the back end as far as resale, though, because you can sell it to an owner occupant OR investor. As far as a multi, personally if all things were equal I'd go for the multi for a few reasons. 1) Added diversification.. if one tenant doesn't pay, you can still cover property expenses with the other tenants 2) Shared capex... typically, one roof and one property to maintain but multiple streams of income 3) Less vacancy.. usually multi's rent for lower, for example one of mine is the sweet spot of 3 bedrooms for $1300. These are usually easier to fill because it's perceived as "better value" versus a 3 bed SFH that is renting for $1800-$2000. There are going to be more people who can afford $1300 so vacancy is less of an issue.
3) This is a broad question, and it really depends on so many factors. As a newbie, I would probably start with one property, and see how that goes.