I do Tai Chi! I began about four years ago, my SO gave me the gift of six months at a class. Ohboy I was filled with huge anxiety, I'm beyond shy and have medical issues so I was positive I wouldn't be able to do it.
Four years later here I am, still doing it lol. I'm doing Taoist Tai Chi, if you Google it you will see it is an international organization with chapters all over the place.
The thing that I love best is that it doesn't matter how bad someone (okay.. me) is at it. It's not like a regular athletic thing with competition, it is all at your own pace at your own best.
It is a strange mixture of simplicity and difficulty which really sums up Tai Chi as a philosophy now that I think about it. Equal and opposite, yin and yang. The more you put into it, the more you get out of it.
If we don't have a chapter near you I'd try other ways. Some retirement communities will offer it (since it is great for older people due to the lack of force in Tai Chi), adult classes at the high school, even try your local library.
The problem with doing it at home from a DVD is that posture and foot placement is very important, it's difficult for a beginner to discern that a half inch foot placement really makes that much of a diffference in balance.
I'd suggest at least four months of a beginners class then go at it on your own. You won't be likely to hurt yourself but you'd get a lot more out of it.
Oh! And on YouTube you can find a video of Master Moy doing the series I do. It's very cool!