Well, I'm sure that you've been on the other side of the bar so the names of the drinks aren't foreign to you...
Most of the time, you can ask people about the weird drinks and a lot of the times people will prefer it a certain way. For instance, I like my margaritas a little heavy on the lime juice.
Don't be shy, this is when people are letting their hair down...people like having a friendly face and someone with a good sense of humor. The best advice that I can give is make the person feel as he is the most important person in the world (but remember that you have a bunch of other customers to take care of). People appreciate that, alot. Once you get a following, it's really nice to remember what they drink and when they come in, ask them specifically if they'd like (the actual name of the drink) one. You will not believe how far this will get you.
It really isn't about the drink but how the person is made to feel when he's trying to relax and unwind. You seem like someone who cares about people so you should do great! Best of luck and if you have any other questions, ask away.