Tai Chi is much more than just a slow exercise, although a lot of it today isn't. Most Tai Chi schools unfortunately have come about from someone learning the very basic movements of the form etc, and going off and starting to teach them after a 6 month course.
It takes at least 10 years to begin to understand the depths of Tai Chi. This is not to say that it will take you 10 years to start getting benefits from it, you'll be seeing benefits as soon as you start training.
But if your teacher has only studied with their teacher for a short time, then they will not be showing you the correct stuff, and so all you will get out of the class is some physical exercise, which is still good, but you're paying money for something you could have for free by just going for a walk.
Tai Chi was designed in a way to work every muscle, joint and sinew in the body, while also keeping relaxed in both body and mind. But it has to be done in a very detailed way to get this happening.
The postures also give you an internal cleansing, sending a higher than normal flow of Qi "energy" through your bodies energy meridians. Again with out your teacher having the proper knowledge of all this, you won't be learning the proper way of moving the body to get these activations happening.
A basic guideline, is to learn one of the long forms, as the short forms have been watered down so much, they have lost all of the above. They were designed for competitions in China, to look nice, but are really nothing more than some slow movements that look like Tai Chi.
The more original and pure the style is; the better it will be.