We go most years, for the last 4 years at the end of May beginning of June, its normally extremely humid and can be uncomfortable at times)
We have tried searching our own packages/flights etc, but always find that Virgin holidays comes back at very little extra.
DONT stay on Disney, its a rip off, This[/url]place has always done us well, its near everything (disney, food, shops etc), has bus transfers to everywhere and is clean, comfortable and has decent pools.
You spend nearly all of your time out and about so you dont need much other than a room!
I would buy the 14 Unlimited disney pass so you can use all the facilities as much as you want (Its only £20 more than a 7 day pass) then you can go between parks etc.
I would also get the Orlando ultimate flex ticket for Universal, seaworld, busch garden etc.
A villa is nice (we are doing this again this year) but works out more expensive for a family of 4.
As for Kennedy its amazing,( we have been lucky enough to see a couple of launches over the years) but my kids (6 &12) went for the first time 2 years ago and were bored after an hour.( we loved it when the bro & sis in law had them so we could go!)
Anything else, ask away.