Hi Alison Welcome to the UK DIs.
You will find that TC's are accepted almost everywhere in Orlando and WDW. The only exception I think, may be the vendor stalls around the parks, where they sell Cola's, Ice Cream's, Donut's, Fruit and that sort of stuff. Everywhere else take them without any problem. It might be advisable to try and get lower denominations if you can as this is a lot easier. We have only ever been asked for ID when changing up a $100 TC once, and that was at Downtown Disney. Otherwise we have never been asked for ID in all the 6 visits.
I prefer TC's to cash initially as it is safer, but I do always recommend that you try to get some dollar bills for your immediate use when you arrive, and some loose change is handy for the tolls on your trip from the airport to your hotel/villa and for any tips around the airport. Tipping is quite acceptable (and often expected) in the US - so to have some $1 bills at the ready is worth noting. Plus you have to pay for the trolleys at Orlando Intl. (Cant rememebr if you have to at Sanford, sorry).
We also used our CC (extensively! LOL) and again, they are acceptable at most places without any problems. One other tip - advise your CC company that you are travelling to the USA. They should then make a note on your file to expect $$ transactions. There have been cases where people's CC have been refused because of 'unexpected transactions' - this would save you any embarassing refusals on your card.
We are two adults and I usually take about £1200.00 - £1000 in TC's and £200 in Cash. Also any loose change left from previous holiday. Then CC's at the ready
If you have an American Express card, this sometimes affords you extra discounts in WDW as it is the 'accepted' card at Disney. Might be worth looking into if you think you might be having a spend up at World of Disney in Downtown.
Have fun - as it is your first time, you are in for a wonderful, amazing time!
Let us know how you enjoy it when you get home.
Hope this all helps, if you need any more info - just ask away.