I also recommend bringing along a few closed-cell foam pads and a proper, collapsible backcountry snow shovel. These are two of the most useful, all-purpose tools (and those most often overlooked by novices) that you would use on a more serious winter camping trip later on.
The shovel lets you manipulate the snow. The pad lets you sit down comfortably and keep your things dry. You also might consider investing in a Crazy Creek chair, a handy little sleeping pad that converts into a supported seat. Cascade Designs also makes a version called the Therm-a-Rest'r.
Your choices, in a nutshell, are snowshoes, Nordic skis, alpine skis or a snowboard. Which of these you choose will depend on your personal style and backcountry goals. Unfortunately, skiing is a skill-intensive business. All we can do here is provide an overview of what's out there.
Snowshoes. The stand-by of the trapper, snowshoes are a reliable and relatively risk-free means of navigating snowy mountains. You're unlikely to take a serious spill using them, but you also can't move as quickly as you could on skis.
Snowshoes underwent something of a design renaissance a couple of years ago, so there are plenty of good models available--and the segment seems to improve noticeably each year. These days, manufacturers pass over wood and buckskin for more durable materials such as aluminum and Hypalon. However, some models are made of a single piece of molded plastic, rather than a mesh design.
In general, look for beefy bindings, a light overall shoe, and a well-designed shape that won't interfere with your walking. The better designs manage to balance the shoe side-to-side, while biasing the profile outward slightly to keep the shoes from getting tangled up.
Larger snowshoes are more cumbersome, but provide more flotation for heavy people or those wearing a backpack. You should also consider the snow you'll likely come across. Light powder snow, like you'll often encounter on a cold Rocky Mountain day, requires a larger snowshoe to support your weight. A smaller shoe is ideal for that wet, slushy snow found on a 31.9 degree-day in the Washington Cascades.
Snowboard/Alpine Skis. Volumes could be written about the fashion statement and personal style differences between snowboarding and skiing--make your best estimate about which kind of person you are. Thankfully, you no longer need to carry a junior-high, student-body card to ride a snowboard.
As far as which is actually more fun, that's also a subjective decision. You can't go as fast on a snowboard as you can on skis. On the other hand, a snowboard can tackle crud and powder in a way skis do only in their dreams. Converts from skiing to snowboarding tend to argue fanatically that the blissful grace of carving on a board beats skiing hands down.
While snowboarding continues to enter the mainstream, manufacturers have also begun to reconsider the ski. Several years ago new radical ski designs took off like crazy in the market--very fat skis for heavy powder and skis with radical sidecut for beginner-friendly carving. You'll find both worth a look. Trick skis are also growing more popular. These are shorter boards with curled-up tips at each end intended to bring some of the snowboarder's free-form aerial stunts into the world of skiing.
The best policy, if you don't already have a favorite, is to try them all. Most people need a few days on the slope, so you'll have to invest in a few lift tickets and rental days before you can really know which you prefer. That's a small price to pay though if you plan to invest in a set of skis.