Initially, it is likely that the style will be chosen for us. It will be the style of the local tai chi class, or the style of the first book or DVD you get. For me, it was the Yang style. The different styles tend to derive from a family who created the style and then passed it down from generation to generation. Yang is, apparently, the most popular style in China. Yang style is a gentle flowing movement, practiced at the same slow, graceful pace. Other styles, Chen for example, have periods in the form of fast paced movement. Yang was the style in the first book I read and so it became my practice from the beginning. As I had begun with Yang I decided to continue to learn the form more fully.
Each of the styles has a number of different forms, of varying lengths and complexities. I decided to learn the Short 24 Form, the Tai Chi Eight Immortals Cane Routine 1, which is Yang style, basic push hands as well as basic common taijiquan and qigong exercises and breathing techniques. It's quite a lot and my estimate is that it will require around 300 hours of training to become familiar with the Forms just listed. And this is just the "tip of the iceberg"! Then there is the more complete Yang long 108 form, Yang applications etc. Then maybe Chen style ... then ...
I think the best advice is to take it slowly. I have read that the ancient masters would have students learn stillness for five years before they began any movement. My above list may be far too ambitious. Time will tell.
Of course, it is not the arrival at a destination, but the journey that is important. Expectations for the journey? A greater sense of health, well-being, balance and centeredness. I'll keep you posted!