Not sure if this is really going to help but I hope you do realize that you cannot just show up one day on Antigua and expect to take up residence. Like many countries Antigua (as is the case with most Caribbean Islands) has complex rules that govern their immigration policies. Simply stated you must apply for residency status before you will be allowed to live on the island. To take up residency you will have to prove that you have the financial means to support yourself as you cannot work on Antigua without a valid Work Permit (these are hard to get - more below). If residency is granted you will have to pay the required fees.
One way you can obtain residency is by purchasing property. A second way is to invest in a business that will provide jobs for the locals. If you obtain residency status by virtue of purchasing property (you'll have to acquire an Alien Landholders license and pay the required fee) you or members of your family will not ability to work without the aforementioned Work Permit. To obtain a Work Permit you must possess a unique skill and your potential employer must demonstrate that there are locals qualified to fill the position. The process can take anywhere from 3 to 6 months during which time you are not allowed to work on the island. The Permit, if granted, is good for 1 year and must be renewed annually (your employer must again demonstarte there are no locals qualified) and there are no guarantees the Work Permit will be renewed. Work Permits are good only for that person and do not extend to other family members - your spouse will to get his own Permit.
The above processes are filled with lots of bureaucratic "red tape" so it would be very wise to hire a local Antiguian attorney to assist you.
As far as schools go, without trying to sound "elitest" if you care about your child's education you probably will want to send your child to private school (tuition can run anywhere from $5,000US to $15,000US per year) rather than one of the government run schools (many Ex-pats send their children off-island to boarding school in the US or England). That's probably why you've gotten comments like "it depends where you live".
It sounds like you've never been to Antigua before. I have a home on a neighboring island and can tell you life on an island is going to be far different from living in Florence. It's not all palm tress and pina coladas. It's not a good idea to move to an island "to escape" from the daily grind because you stillhave to support yourself and family, pay bills, shop, do laundy, cook, etc. My best suggestion is that you use this upcoming trip not as a vacation holiday but rather as a way to find out about daily life. Stay in an efficiency unit rather than a resort. Do your own shopping and cooking, check out neighborhoods and housing accomodations, do laundry, drive around during "rush hour" so you get a feel for what it is like to commute, explore potential job opportunities, check out utility costs, explore island amenities to see if they meet your expectations. In other words try to approximate everyday living rather than spend your time sitting on the relaxing on a beach. A lot of the modern conveniences you come to expect living in a big city are not readily available on island. Island life is not for everyone. You'll find housing costs will probably be higher and wages (if you are lucky enough to get a Work Permit) will be lower. Do as much reasearch as you possibly can. Scour the internet and the library - plenty has been written about moving to and living on an island. It's all ot there you have to look for as no one can tell you if island life is right for you.