We are flying to Florida to 3 weeks. To avoid delays at the airport am I better off only taking a carry-on on the plane and shipping the bulk of my clothes?
Sounds a bit extreme - its not THAT much of a delay typically, especially when compared to the hassle of shipping your clothes and re-uniting with them in a remote land.
You will still have to queue up to check in (with most airlines)
By the time you have gone through immigration at the far end (the main delay and you can't avoid it) your checked baggage will usually be waiting for you.
And it will cost you a bomb to ship your clothes and if you are unlucky will get stung for duty on them (maybe a bit unlikely but possible)