I can understand why you would want to see these places and they're all totally unlike each other.
As stated, St. Barth's is beaucoup Euro - very lush and lovely, and it's here you might shoulder up to the bar and rub elbows with who knows who of the rich and famous brigade. Be prepared to spend lots of money for the simplest of trappings. Getting there from St. Maarten/St. Martin involves either a boat ride, which many say is not for those with weak sealegs, or a flight from either Grand Case or PJIA, the latter of course being the faster choice but the waiting around time to me, anyway, seemed worse than the boat ride. And I have to say, I had no problems with the boat ride over and loved the ride back.
Next possibility - Anguilla and one of my favorite islands. We often give up 3-4 of our St. Maarten days every April to overnight here. It's no where near as beautiful as St. Maarten or St. Barths but the beaches are the most incredible beaches in this part of the Caribbean and many say of the world. My travels haven't taken me far enough to make that comparison but we do love it there. And don't let anyone kid you - the rich and famous are there, too, but they're aren't as open to being seen and you usually have to frequent some of the higher end hotels and restaurants to rub elbows with them. As far as costs, you can spend high or low and have a great day either way.
St. Kitts and Nevis - ah, it's been a few years but these are two very different islands. They're not remotely as easy to get to and will definitely require a flight and probably would be more enjoyed if you were able to do a stay over. There's lots of history to be enjoyed and the Fort at Brimstone Hill is not to be missed if historic sites are your thing. The beaches, IMO, do not even remotely compare to those of your other two choices or SXM, but they're quite doable. St. Kitts boasts a beautiful black sand beach but again, this wasn't my personal cup of tea. I don't think it's remotely as expensive on these two islands, or at least we didn't find them to be, but it's also been a while since we've visited there. St. Kitts and Nevis are scenic and beautiful but IMO require a little more time and in order to enjoy the best of both you'll probably spend a little more money but you'll end up feeling like you've gottem a lot more for it.
And lastly, if you want to take a walk on the wild side - a totally different Caribbean experience if you're willing to give up a day of beaching, is a trip to Saba. (There is a beach there occasionally, but I wouldn't go to Saba for a beaching day.) It's about a ninty minute boat trip which again, many find to be gruelling, or a ten minute flight in a STOL type airplane - the landing of this is an absolute experience in itself. The island is immaculate, lush and incredibly beautiful. Scenic and a photographers dream but definitely NOT a beaching island. The latter is worth a trip just to say you've visited a Caribbean volcanic island. The first time we went we took the Edge out of Pelican Marina and that trip was enough to tell us we wanted to go back again and explore a little more on our own. It's a unique island but may be way out of the realm of what you're interested in.
As for the SXM weather forecasts - they almost always read cloudy with a chance of rain but over almost forty years of visiting annually, I've yet to experience a rainout. Not to say they don't happen but they've not happened to us over all those years and all those trips.
Don't know if this is the kind of info you're looking for and if it's a first trip for you, you may just want to let sand gravity take control and save the island hopping for another trip. Whatever you do, relax and enjoy.