You'll probably get this answer a lot, but it depends. I can't weigh in on the best time of year to buy property in Sarasota, but turnkey or rehab I can speak to.
For your very first property, if you have enough cash saved up and not a lot of experience doing any rehab work, I think going turnkey is a totally fine way to go.
To get started, determine your criteria. Are you looking for single family houses? Duplexes, triplexes, quads? Are you looking for 3 bedroom or 4 bedroom units? You get the idea. Then, get pre-approved by a couple of lenders. Next, go to a few agents, share your criteria with them and your pre-approval and start receiving properties to review. Also, start working with wholesalers and network with property managers to try to find deals that are off-market.
If you're shorter on cash and have some background or at least a strong willingness to learn the rehab process, doing a rehab could be the better way to get started. In this case, determine your criteria first, just like you would for turnkey. Then, instead of conventional financing, look into hard money or construction loans through small banks and credit unions. Then you'll need to start vetting out contractors to work with around the same time you start working with agents to find deals for you. If you'r doing a rehab to start, driving for dollars makes a lot more sense than if you were goin to do turnkey.
Best of luck!