Sounds like you have a good plan. A lot of out of state people look to our area, and there are several good agents and property managers you can choose from.
If you are wanting to learn our area I'd suggest looking at 61st ST and Yale Ave on google maps in Tulsa. Saint Francis Hospital is nearby and is a larger employer. If you're wanting B class, turn key, not a lot of issues that come with historical homes, this area would be good for you as the properties tend to be 1960's or newer.
If you are wanting to be near other good hospital employers, but are willing to take on something older with "historical charm" then I'd like near the University of Tulsa, which would also double as a benefit of being able to pivot to student friendly LTR rental style should you need to. Besides being near TU you are also near downtown and good pockets for hip, fun things to do like the growing Pearl District, Mother Road Market, etc.
I personally haven't done MTR just yet, but I can say as an observation I've worked with a growing amount of buyers who stayed in an AirBNB / MTR type of place because they sold their house, or moved to Tulsa. Certainly, population migration has benefited Tulsa in this regard.
I wish you well and am stoked for you to consider T-town on your investing journey!!!