You can get a temp tag from NC, or a trip permit, etc, however find out the FL req for licensing. There is a grace period where you don't need to have it tagged after purchase, just keep bill of sale w you.
I'd just buy it and drive it home, not a big deal at all.
Contract? Not sure what you're talking about. Get the signed title, and a bill of sale. End of story. Or a doc from the bank if the title is currently held by a lender. You're unlikely to get the title released instantly unless its literally a small local bank physically holding the title locally.
Is this the first vehicle you've purchased? Out of state makes no difference than in state.
2016 Ram 2500, MotorOps.ca EFIlive tuned, 5” turbo back, 6" lift on 37s
2017 Heartland Torque T29 - Sold.
Couple of Arctic Fox TCs - Sold