[timprov]

When you're starting out, definitely each get a glass of what you feel like. Offer to let her taste yours, and hopefully she'll reciprocate.

I don't have much time for the popular varieties in this thread, personally, so I don't have anything to add to specifics. The most important thing is to keep records of your results. A wine log is very useful when you're trying to remember just what the name was of that one you liked so much.