It really depends on what you are looking to get out of your vacation, and what time of the year you will be going.
If all you want to do is be lazy and veg out on the beach all day, go with the Gulf Coast from about Clearwater/Tampa on down. The beaches are fab and it is hot year around. The water is very warm and the surf is very gentle compared to the mad waves, cold water and rough surf of the Atlantic Ocean. I have swam at lots of Atlantic beaches from Ft Lauderdale to Palm Beach to Miami Beach. I usually get out after 5 minutes as I get sick of the rough waves knocking me over, the very strong under currents, and the very rough shingle underfoot that will cut your feet to ribbons. The water gets deep very quickly, and is not kid friendly at all.
Avoid the Florida Panhandle. Prices there are cheaper, but it is where folks from Mississippi/Georgia/Alabama go for a beach hollier, as opposed to peeps from overseas. It is not called The Redneck Rivera for nothing. It is also NOT hot year round there. Florida is over 700 miles from north to south. That affects the weather. In the north of the State, it is not unusual for day time temps to be in the or 50's or 60's Nov to March. Not beach or pool weather at all. If you are making the trip from Ireland in the winter, and are expecting it to be hot you could be in for bad surprise. I have been in Daytona, Jacksonville and Orlando in Jan & Feb & they were not warm at all. Only in the lower third of the State are you guaranteed hot weather all year around.
The east coast has more to do and see overall, but prices will be higher, especially the closer you get to Miami. Do you want good shopping and fancy night life and lots of touristy things to do? If you do, then go with the east coast, as the west coast is quieter. Tampa/Clearwater/St Pete are nice, but you can see what they have to offer in about a day each. Miami is where the real action is at, and has a real buzz to it that you get off all big cities. I know Florida very well. I live up the road in Georgia, so holler if you have any more questions.
PS Factor in the cost of home owners insurance to your yearly bills. It used to be fairily cheap, but after all the hurricanes from 2005-2007 the costs have sky rocked. It used to be a flat rate per year, but now it is a percentage of the value of your home. I am not certain, but I think it is in the ball park of 5%. Hurricanes themselves are most common from mid August to mid October, so if that is the time that you are going, get really good travel insurance in case your flights are affected by airport closures or delays. Unlike Europe, airlines operating in the US are under no obligation to reimburse you for expenses incurred if your flights are canceled or delayed due to the weather.