You asked "what i can expect to do in classes, and what i can expect to achieve from it long term?"
What you do in classes depends on what style of Tai Chi it is and whether or not the classes are geared more towards health or the martial standpoint.
If the classes are geared towards health you can probably expect to do the form mostly and some Chi Gong.
If the classes are oriented towards the martial side of things it will depend on how much of the system the teacher has. Hopefully they will have a Nei Gong set (internal power training) Chi Gong, form work, 2 person sets, and maybe even some weapons training (straight sword - spear - staff).
I see that you are a boxer, have you looked into Xingyi at all? I would think that for a boxer Xingyi would be a great cross-over martial art for you. Maybe check out Aarvo Tucker's site www.palmchange.com
- I believe he primarily teaches Gao Style Baguazhang, but he may throw a bit of Xingyi in there.
As for the long term benefits, Neko pretty much summed it up. Relaxation and integration of the entire body, balance, and peace of mind are all great atributes. Personally I think that Taichi effects everyone differently.
Newbe101 - Fajing is described as "explosive internal power" i.e. Bruce Lee's famous 1" punch. There is no way that you could possibly learn this from an online course- it is something that must be directly transmited from teacher to student, and even then it is a high level piece of the internal martial arts curriculum. If you are seriously looking for a teacher, let us know your general whereabouts and age.