The answer really depends on how many fish you want to catch. If you are happy being in the tropics, wading in warm water and drinking beer.....you don't need to be much of a caster. If you want to catch bonefish or permit.........you better learn to cast.
A DIY bonefish fisherman is typically walking the flat and not casting from the front of a boat. One of the advantages of walk and wade is you can normally get closer to the fish and don't need to cast as far.
Ideally you can cast 60 feet into a mild wind and 40 feet into a strong wind landing your fly inside a hula hoop.
You should also be able to load your rod quickly, false cast no more than twice and fire!!
To become a good flats fisherman you need to do two things well:
Seeing the fish can be frustrating but the more time you spend on the flats the better you will get at seeing the fish and/or seeing the signs of fish (nervous or pushed water). I have spent a lot of time on the flats and see fish fairly well but compared to a guide who has been doing it all their life, I come in a poor second. It helps to fish with guides or experienced flats anglers and learn their tricks.
A couple of helpful ideas for seeing bonefish: pick areas where the flats are clean white sand, much easier to see fish on these flats rather than over turtle grass. Fish the evening or twilight hours for tailing fish, some people see tails on the surface much easier than fish in the water column.
There is limited access to information on DIY flats fishing but after you look at what is available at DIY Flats Fishing you should check out The Bahamas Fly-Fishing Guide and The Angling Report. You can also get some help from the fishing forums.
Tides are extremely important when fishing the flats. Bonefish typically follow the incoming tides to their feeding area and leave the flats for deeper water on outgoing tides. When the moon is full or dark (spring tides) the high tides are higher and low tides are lower, during a quarter moon (neap tides) the tides are more even. In some places the high spring tides can mean the fish are well into the mangroves and can't be reached and off the flats on the very low tides. Neap tides allow better access to the fish and the fish remain on the flats for a longer period. I would recommend Randall Kaufmann's description in his book Bonefishing to better understand how tides effect fish on the flats.
This is a tough call. For strictly DIY bonefishing there are relatively few places that provide both a great family vacation and good fishing. Abaco is a good middle ground and Exuma can be nice if the expectations of the family don't go far beyond snorkling and nice beaches. But without knowing your individual needs I would pick Provo in the Turks and Caicos as providing the most amenities and fun for the spouse/family while providing real opportunities to catch bonefish on your own.
If you have never been to the location before I would book a local guide for the first two days.
This depends on your abilities and desired level of comfort. Overall I would point you to the Bahamas for your first DIY bonefishing experience. Exuma is an ideal place for DIY fishing but the fish themselves can be picky. Eleuthera is good with lots of flats but the bonefish can pe spooky when fishing the more well known flats. Acklins can be good, lots of fish, lots of flats but a little rustic.
I have mentioned this in other sections of the website, but in a nutshell pack your carry on as if your luggage will not arrive. In the last four years this has happened to either myself or members of our traveling group, it happens. So make sure you have your prescriptions, rods/reels and whatever clothes (including wading boots) you need on the flats.