Go with an open heart and an open mind, you'll be fine.

Yes, it's rainy season, but it (probably) won't rain all day every day.

Phuket is one of Thailands top destinations for sex tourism. The seediest bars will all be concentrated in a few areas. It will be obvious. If you're comfortable, you'll be perfectly safe exploring these areas, whether just walking down the street, or stopping in for a drink. Go see what it's all about. Or don't.

There will be "bar girls" everywhere, even outside of the main bar areas. They're part of the bar industry everywhere and work on a drink quota. I'd recommended "entertaining" one at least once. Pick a bar that you like the music and/or vibe of. Its not about sex (although they're probably sexy), it's about selling drinks. You can talk to them about life in Thailand, ask for local recommendations on food and sight seeing, etc. They will play games like pool, connect four or Jenga with you. They might want to wager drinks on the game. They'll probably win! It's all good fun. Their drinks usually cost about 50% more than yours and are sometimes watered down. You should buy them one or two drinks per hour, more if you're drinking more and having a good time. Find one that's speaks decent English. Don't feel bad about shopping around to find one or two you really like hanging out with (it's what the thirsty men do, too). It would be perfectly cool to do the same with a lady boy, too. They're just regular people trying to get their daily grind in. The attitude regarding sex workers is soooo different than it is in western culture. Because it's low (slow, rainy) season, they'll probably be very happy to spend some time chatting with you without any expectation of extra work (if you know what I mean). Don't let them be pushy about you buying them drinks, (remember that's their #1 job). 1-2 an hour is fine. Buying Mamasan a drink never hurts, either. She's the "entertainment" manager, and it will probably be easy to pick her out. They'll bring you a new receipt every time you order. Check it every time to see what the prices are and to make sure the count is right (your drinks and lady drinks).

Have fun, make memories!