Look for someone you enjoy being around and can communicate with. Avoid people who horse around in the gym or don't seem to be paying attention while belaying others. A class is the best place to meet a partner. Your skill level will be the same, and you will have learned how to communicate together. Once out there, don't be afraid to take a lot of time on a route and to learn for yourself how to do things.
Ratings are for egos.
Start with sport climbs because the ratings are similar to the gym. Start low around 5.7, and work your way up. Make sure that you are safe at all points. We'll probably be getting up to 13,000 feet. Spread the altitude gain out slowly.