When you buy a harness, try it on over your jeans, or fleece pants. Make sure the belt and leg loop adjustment gives you a couple of inches to spare, for cold weather clothing or one too many Lasagna dinner. If your local climbing shop has a climbing wall, put on the harness, clip into a fixed line, and hang. Ask the Expert or go to GORP's Climbing Forum to exchange information on climbing destinations, partners and much more. Try GORP Travel - Climbing for climbing trips and schools.
Harnesses weigh anywhere from two thirds of a pound to a whopping two pounds.
Lighter is better, but don't compromise comfort for a few ounces. The features you need in a harness depend on what type of climbing you will be pursuing. Standard features are a belay loop, a haul loop, padding, and reinforced gear slings. You might save a few dollars buying a stripped down sport rig with limited racking capabilities, but both use and comfort will be limited. The ability to micro-adjust a harness, depending on what you are climbing, and what your are wearing, is extremely handy.