I'm a runner and I swear by waxing. Actually, I had my bikini line lasered about a year ago and that was the best investment ever. It was $600 and it is permanent. Of course, you don't have time for that at this point, plus you might not want to make that investment.
So, back to waxing. Even though I had the bikini line lasered, I get everything else waxed. Yes, Brazilian. Sorry of that is TMI but I know the first time I had it done I would have been a MESS and completely lost as to what to expect if I didn't have my girlfriend to talk to. So, in the same spirit that she told me everything, I am answering you.
The advice you have already received is excellent. High end spa, for sure. That way you know the person will be licensed and experienced. And if you are at a higher end spa, they will automatically use the right wax. You need hard wax for most areas, but there are a few areas where the softer wax is necessary. A good technician will use different waxes on different areas and/or different types of hair.
Ideally, you could have tried it out before and then get a second one right before your trip, but since we are only 3 weeks out, I would go 3-4 days before your trip. That way, any redness or irritation will be gone by the time you get to FL.
As for running, I LOVE the difference. Again, this might be TMI but I know that this is an embarrassing topic, so I'll just put it out there-- First, the sweat issue. Sweat clings to hair, right? Like at the back of your neck, etc. Well the same happens in "that" area. And I would have a damp patch and it was uncomfortable. And although I always wear black running shorts or tights, I always wondered if it would show through if wearing a lighter color. No one needs a wet spot right there, kwim? So, having it waxed completely eliminated that whole issue. I feel so much more "clean" if that makes sense. Secondly, there is no chaffing! If you are someone with coarse hair or just a heavy growth pattern where you have hair into the crease where your leg meets your groin, you can get some serious chaffing during those long runs of 8+ miles. Again, with no hair there, this is a non-issue. And of course, you don't have to worry about a thing when you put on a bathing suit.
If you have any questions, ask away! I know it can be a personal or embarrassing topic, so what better place to ask these types of questions, right?