We were just in Florida this September/October - actually for our Honeymoon :-)
It is difficult to fly direct from Edinburgh, I think there are flights but not all year round and can be more expensive.
We have been to Florida a few times actually. Flown from Glasgow 3 times and Manchester once. I have also booked through TUI, Thomas Cook, and Virgin before. I prefer Virgin as the extras and general level of service is higher, but so is the price.
Thomas Cook is usually the cheapest but we didn't have a great experience with them so likely won't book again with them. Likely a one-off, but yeah.
We had planned on getting to New York from Orlando but just ran out of time. It is fairly easy to get a flight to New York from Orlando, you will just need to do some planning etc.
Hotels... Disney hotels are expensive and usually don't offer anything more than other hotels at Universal Studios or Internation Drive (Main tourist area). The best hotel we have stayed at was the Universal Aventura, it's very affordable and the hotel is very nice, modern and has all the usual facilities you'd expect. Not to mention walking distance from Universal parks. Disney can be the slight issue as they don't run buses to Disney from Universal, but we found Lyft and Uber would get us to Disney faster than any bus and usually cost around $10 to $15 for the whole family.
As for tips... Buy your park tickets while in the UK from UK authorised sellers. Buying in the USA is very expensive.
Make sure you plan proper rest days, even just days that are slower and not in the sun all day. It can really get exhausting at the end of a two weeks on Florida without a few days of chilling out. We usually have our rest days at Malls and just take it easy and that works for us, but even a day at the pool would be awesome!
Another tip would be to book fast pass for rides you really want to ride. Some days can see the new Avatar and Toy Story queues jump to well over 2 hours. There is a snow white roller coaster which is always above 90 minutes wait times when we visit.
If you have any questions just let me know. My friends and family know me as the Orlando expert :D