Welcome to Sailnet and congrats on being bitten by the sailing bug!
As I've read your plans, it seems to me your near- and long-term boat requirements are different. My suggestion would be to focus on a boat that is ideal for the lake sailing you plan to do initially, perhaps with the ability to tow it over to the coast now and then to expand your range and learning opportunities.
When and if the opportunity to head out to the Bahamas and beyond fully materializes, you could then look for something better suited to that sort of itinerary and venue. This will give you time to gain experience and better understand what your requirements are, as well as to evaluate the trade-offs of various designs.
I have a strong preference for diesels inboards, but for lake sailing, I definitely would not rule out outboard engines since that would eliminate most of your best candidates. When you graduate to a larger coastal/ocean sailor, yes, look for a diesel inboard.
One thing you need to confirm is the maximum draft that your lake can accommodate at the launch ramp and for sailing around. Some areas are very shallow, requiring a centerboard arrangement.
If you have good water depth, one boat I really like in your price range is the Beneteau 235
. It can be a good family lake sailor, with weekend/cruising capability, as well as trailerability. These also have a nice degree of responsiveness and performance, which is especially helpful when learning. They come with either a wing or fin keel. Either is good enough. Anyway, that's a datapoint for comparison as you move forward. Good luck!