I'll second what teachskiljp said: Don't wait until March, if you can get out to the mountains earlier. Our season begins in early-mid November at Breckenridge and Keystone, so there's lots of winter to enjoy and improve.
Please consider taking some lessons - we have a great ski school at Breck (and also at Keystone). Several of us here are on staff at the Breckenridge Ski and Ride School (skier31, chuckc, myself and some others) and a number of other Epic folks are instructors at some of the other mountains in and around Summit County. It's often the best way to build confidence, gain skills, and have fun while you're exploring the mountain. Even if you can't make your next ski vacation until next March, a few lessons early in the week will have you enjoying your ski vacation a whole lot more.
Lots of different places for a beginner to ski; at Breck, Peak 9 (the base areas closest to Main Street and downtown Breckenridge) is probably your best bet. We have base areas at the Village, and a little ways up the hill at Beaver Run. Most of the lower part of Peak 9 has long, gentle wide green runs that are great for learning, plus easy access to some more contoured greens and to blue intermediate trails when you're ready.
Some of the lodging downtown could be considered "walk-to", as are some of the lodges on the road up to Beaver Run. The more upscale lodging at the Beaver Run Resort and at Breckenridge Village is ski-in/ski-out. There's also easy access from pretty much anywhere in the County from the free Summit Stage to Breckenridge, the town's Breckenridge Free Ride bus, and the resort buses.
Also, if you might consider a trip to Utah in late January, consider the EpicSki Academy
. The organizers and coaches have often said they're hoping to get more beginning skiers at the event, and that would be a terrific way to learn from some of the top pros in the business while having a hugely great time!
One way or the other, hope to see you on the hill!