My suggestions, and we welcome you to Sunny Fla.....
This is not complete but is a good baseline. Keep in mind that WATER is your number one threat, followed by fire.
1. Turn off the hot water heater (drain it if it's inside the house).
2. Shut off any water feeds to the washer. Ideally shut off all water at the main source.
3. Unplug both the washer and dryer.
4. Turn off all ceiling fans.
5. Shut off any gas
6. Before winter, check to see if your pipes are insulated. Consider using RV antifreeze fluid in your drains (don't use regular auto antifreeze!!).
7. Close all drains in tubs and sinks
8. Open the lids to the toilets and place saran wrap over the toilet bowl (if the water evaporates out of the trap, the sewer gas will enter the house).
9. Leave NOTHING in the fridge. Ideally, you will want to clean it out, leave the doors open, and turn it off and unplug it.
10. No food in the house unless it's in a Can. Don't leave bagged items. Rodents can identify a bag by smell, and will get into it, even if they don't know what's inside.
11. Cut back any vegetation well back from the house.
12. Clean the gutters.
13. Drain anything outside. If you have a pool, suck it up and get a service. You can't drain it, you can't leave it alone.
14. Unplug anything left.
15. Leave nothing inflammable in the house....this includes oily rags, some cleansers, etc...
16. Some people would tell you to shut down all the power. I disagree and would leave the AC/Heat on as you have said. You can run it up to 88 easily, wouldn't go beyond 90 as any wallpaper will start to peel. The AC also removes moisture which can be a problem in some areas. Do not let the temp in winter go below 40. Absolutely not below freezing.
17. Take the time to CLEAN THE ENTIRE HOUSE!! I mean top to bottom....floors, fixtures, shelves, cabinets, baths, moldings, baseboards.....EVERYTHING.
I would modify any of these if you have a Realtor coming in to show or check the place based on how often you have that happening.
Finally,
18. Enjoy new digs!!