Wow, I was surprised and pleased to see this thread! I did a lot of fencing in college, for about 5 years. Not a team, just a club doing it for fun. Went to a couple tournaments, did ok. I haven't done any fencing since I graduated, which is... um.... about 10 years. I've actually been thinking I'd like to get back into it, but just haven't really pursued it yet.
Ok, on to the questions... Like you rickg, I've never had any interest in the usual sports, but I loved fencing. So that might be one mark in favor of fencing for you.
I would say it
can be a bit physically demanding, but it doesn't have to be. Depends on how you do it. I heard someone describe it as a fast-paced chess game, where you don't have to wait your turn.

For example, the best fencer I ever sparred with: Probably 60 or so, not in incredible physical shape, not especially agile, etc, but I would swear he could read my mind. I don't think I ever got anywhere near hitting him, he just always knew what I was going to do. I've seen some great fencers with various physical disabilities too. There's a lot of flexibility to take advantage of whatever you've got, compensate for your weaknesses.
I'm surprised you didn't ask about safety, that's usually the first question we got from new people.

I heard that statistically, fencing is safer than golf. Sore muscles, sprains if you're careless. Oh yeah, it's not a bad idea to wear a cup,

if you find it comfortable enough. I've heard of a couple freak accidents, but never saw any serious injuries myself. Good protective gear is essentially a lightweight bulletproof vest/mask. We used to joke that there aren't many injuries in fencing, but when there are, they're spectacular.
Cost... I bought my own equipment, on a college student's budget. If I remember right, it might be 100-200 for a good mask, same for a vest, and 20-50 for a weapon. Clubs will often have stuff you can borrow too.
If it intrigues you at all (and obviously it does, if you bothered to post the question) I'd definitely give it a try. You may be able to hook up with a local school club, or find a commercial club.
BTW, If anyone in the Atlanta area knows of a good place to fence around Marietta, Roswell, or Alpharetta, please let me know.