Most overseas investors that I have bumped into tend to fly to the city they are investing in quite frequently and really learn the players, the market and their investments. 

I don't mean to be rude when I say what you're planning would be like someone saying they want to develop their skills as a pilot by buying a plane and flying it alone before going to flight school.My tip for you is contract a PM.  

I have two others in Raleigh and one other in Jacksonville, Fl. I

When things begin to drop, those typically fly out of Houston for the Keys or somewhere nicer, will settle for Galveston.

I'm tired of paying for apartments when I fly into town.

In FL, I used twice Rooms to Go 5 years no interest, pay back in equal installments.  

For real estate, since you will only be operating in the state of FL, I believe you need a FL LLC.

My market is tampa, fl. I

I do plan on flying into Indiana next 1-2 months for something. 

I currently live in California, but grew up in Cape Coral, FL. I