Greg in Hotlanta.
But seriously, any good resort will have a ski school that should be able to teach the basics. In fact, some (like Ski Liberty in Southern PA) guarantee that you will learn the basics of skiing in an hour + lesson or your money back. A good ski instructor will have you standing, walking, moving, stopping and turnining on a pair of skis in the first lesson or two. It won't look pretty like those ski videos everyone sees but it will work.
You may want to call Snowshoe first to inquire about "learn-to-ski" packages. Most areas will have them and they generally include a lift ticket and equipment rental in a package price that's cheaper than paying for everything separately. Make sure that you get a PSIA certified ski instructor (PSIA = Professional Ski Instructors of America). PSIA is a nationally recognized organization that sets minimum standards for ski instructors. A level 1 instructor is fine.
Skiing skills and snowboard skills are very different. You can probably learn both in one day, but I wouldn't recommend it. You'll be sore enough from using new muscles or old muscles in different ways just from one or the other. Also, what you learn in one at the beginner level doesn't necessarily translate over to the other. Pick one (skiing or boarding) and throw your energy into that one. Once you've got a full day (including lessons) on one, then consider trying the other.
Finally, there's a great article on learning how to ski written by a friend of mine who is a PSIA Level II (ski-god) Instructor at Ski Liberty. You can find it at http://www.dcski.com/news/1999/01_30_99/learning.shtml. It's got pretty good info despite who its written by!!
Good luck and have fun!!
In my experience, The learning curve for snowboarding and skiing are the same at the very beginning. I most certainly would not try to learn both in one day and think overall that you would be better off to pick one and stick with it until you have some experience. You really can't evaluate one or another until you have a little mileage under your belt. If you want to switch later, there is nothing to stop you. I know a lot of people who do both.
Can't help you on Beech v. Snowshoe.
I've never been to Ski Beech, but it's hard to go wrong with Snowshoe. For the past two years, DCSki has had an annual survey allowing readers to rate the local resorts in areas such as best terrain, best snow, best for families, etc. Snowshoe consistently ranks right at the top of most categories, and it's a good place to learn skiing. If you're learning, it's always best to visit midweek - there will be less crowds, and at least for me, one of the scariest aspects of learning to ski (or even skiing now that I'm advanced!) is *other* skiers on the slopes. As a beginner, you have enough to worry about without constantly fearing that someone will run into you! So, midweek = less crowds.
I have to strongly echo what others have said: sign up for a group lesson instead of relying on others to teach you. PSIA instructors spend a lot of time learning how to teach beginners, and they have an endless supply of patience.
Learning to ski is a *blast*! For me, it was very rewarding, because you can see a measurable increase in ability each time you ski. For example, my first challenge was conquering the easiest bunny hill - it seemed pretty challenging at first, but once I started to get the hang of it, I began glancing over at the next-most-difficult slope. Before too long, I was ready to tackle the intermediates - and when I made my first run down an intermediate, I was swept with an incredible sense of achievement - and a desire to make it to the experts!
I can't say that everyone has this reaction to skiing. I've taken friends for their first time and they had no desire to go back. I think that's fairly unusual.
I guess one piece of advice I would give is to take your time learning - don't try to advance too quickly. Learn the proper techniques and put in plenty of practice, otherwise you'll learn bad habits and find yourself on a slope that is too challenging to be fun.