You don't need loads of clothes as most people in Florida dress 'casual'. This means shorts or a thin skirt and T-shirts during the day in summer and perhaps some trousers and a sweater or cardigan for the evening in spring, autumn/fall or winter.
Your rental home will have a large washer and dryer available for your use. The wash cycle is much shorter than in UK washers so you can have things washed and dried within a short time.
Leave some space in your suitcase as you'll probably want to buy clothes which are cheaper in USA such as jeans, T-shirts, etc. You won't want to have to buy another suitcase to get them back home in!
The one thing you will want to pack is at least one pair of comfortable shoes! If you're visiting the theme parks, you'll do a lot of walking (you won't notice as it's so interesting) and comfortable shoes are essential. If you find trainers comfortable, these would be ideal.
You don't need to take towels with you (check if your rental home also includes pool towels, otherwise you can take your own or buy them in Florida) or face flannels/washcloths as these are generally provided for you.
You may not need to take hairdryers as some rental homes have these provided too (check with your rental home owner).
Don't take food as you will sign a Customs declaration that you don't have any with you when you enter Florida. Almost all foods available in UK are also available in Florida and you will find a huge selection at the supermarket. You may find that your Florida rental home owner can arrange some welcome supplies for your arrival in your home so please ask them if this is available. If you have a special diet, ask your Florida home owner if this type of food is available, i.e. goat's or soya milk is available in Wal-Mart and other large supermarkets.
You'll need personal items, shampoo, sun tan lotion, etc as these are not supplied but you don't need to take loo paper as at least an initial roll is supplied and UK 'thick and fluffy' toilet paper is not good for American plumbing, which is half the size of that in the UK.
So, don't pack the kitchen sink (there's one provided for you!) in your suitcase and, if you've any doubts about whether something is supplied already or not, just ask your Florida home owner! They will be an expert on what's available in their home and in Florida as they will probably have been there many times.
Don't forget your essentials and make sure these are in your hand luggage - any medication you are taking and a written note of what this is (your GP's repeat prescription request form is ideal if you have these), your passport (which should have 6 months to run after your return), your airline tickets, your car rental vouchers, your travel insurance policy (make a photocopy of this and leave the photocopy at home), travellers' cheques (make these the US$ type and it's useful if at least two of you have a supply in case of emergencies), your credit cards (almost everywhere accepts these) and your driving directions to your Florida home or where you will pick up your home keys.
Last of all, remember to have a great time in your Florida rental home!