I'll assume by "casual" you mean leisurely and are not referring to a partner of the opposite sex, but either way there's no reason you can't each carry your own one man shelter rather than sharing a tent with someone whose unpleasant habits you may not be familiar.
Regardless of the length of your first trip, taking up backpacking as an outdoor activity could wind up costing you a lot, both in money and unneeded effort, if you listen to your elders, your childhood experiences in the outdoors, TV and movies, and major outdoor manufacturers and retail stores, and fail to take into consideration modern lightweight backpacking innovations and techniques which allow people to survive and thrive in the outdoors carrying considerably less weight than you might imagine. The days of huge backpacks, canvas tents, carrying axes, frying pans and folding chairs are long gone, but so are the days of 7 pound heavily padded backpacks, huge nylon tents, heavy leather boots, white gas stoves, and mummy sleeping bags. My family and I don't carry any of those things and we go on week long backpacking trips in the High Sierra. A good introduction to lightweight backpacking is this website: http://www.the-ultralight-site.com/index.html, this message board: http://groups.yahoo.com/group/BackpackingLight/, this store: https://www.backpackinglight.com/, and this book: http://www.amazon.com/Lighten-Up-Complete-Ultralight-Backpacking/dp/0762737344/sr=8-1/qid=1168796878/ref=pd_bbs_sr_1/102-0601339-3354515?ie=UTF8&s=books
There are probably different regulations for different sections of the Appalachian Trail which could entail obtaining free permits at ranger stations before entering the woods, restrictions where to camp, restrictions on storing food against bears (bear boxes, bear canisters, hanging food) and campfires, also depending on the weather and time of year. You'll have to make arrangements to pick up food along the way to resupply, and arrangements for someone to pick you up, and consider points along the way to bail out if something goes wrong. Here's the place to start planning your route: http://www.appalachiantrail.org/site/c.jkLXJ8MQKtH/b.715465/k.9731/Hike_The_Trail.htm
If you have time Bill Bryson's Appalachian Trail experiences in his book "A Walk In The Woods" are a good warning of what not to do: http://www.amazon.com/Walk-Woods-Rediscovering-America-Appalachian/dp/0307279464/ref=sr_1_6?ie=UTF8&s=books&qid=1224894230&sr=8-6
