I have some cross country ski coaching credentials and raced somewhat competitively through high school. I would totally recommend getting into the sport, its fun and an awesome way to stay fit. I have no experience with biathlons specifically though. A few things I would recommend though:
For Classic Skiing
Start on waxless skis and work your way up. Classic skiing is extremely frustrating on waxed skis until you build up some good technique. After you have a good technical base, you can really cruise. I would recommend getting 2 or 3 hour long lessons if you go for the waxed skis, as well as visiting a waxing workshop. If you're getting backcountry skis for exploring, they probably have fish scales (waxless) and are a good start but not something you'll be flying down the trails on.
For Skate Skiing
This technique can be hard to get the hang of at first, there are some subtleties with timing/when to use difference techniques. The plus is that you'll be cruising around from the start feeling like you're moving somewhere. Again, lessons will help get you on the right track, and you probably won't need many. Only one or two and you can probably figure it out from there.
I would recommend getting an entry level race ski to start on, and upgrade once you're more committed to the sport. Most places also have fairly good quality rentals that you can try out for your first couple go arounds. Just make sure the guys at the shop get you the right size skis/poles or you'll have a bad time.
Boots are one of the most important purchases. You'll want to consider what binding system they are compatible with (profile, pilot, nnn I think are the main ones) as well as the fit/support to warmth ratio. Generally, really nice expensive boots that you'd race in aren't the warmest for slowly tromping around the trail.
XC skiing can be a ton of fun though. Go to a good shop and make sure the salesman knows what they're up to and let them take you through the motions. Take some lessons to make sure you're doing it right, especially if you want to get into some racing. But the most important thing is get out bushwhacking or on the trails and have some fun.