Yes, it is a tremendous advantage to have a laptop at TBS. There is currently no high speed internet access at the TBS BOQ, but they are supposedly getting DSL "soon". You will need to dial up if you live on base as of now.
If you are a married brownbagger , you can get high speed cable like I did.
You will need to type out and print assigments from time to time. Also, you will find that a photocopier in addition to a printer comes in very handy-- so spend the extra money and get a printer with photocopying capabilities.
It would help to have a laptop with DVD capabilities, for the purposes of standing duty. You will have the opportunity to be the "duty" several times while at TBS, which means you will basically sit behind a desk staring at a phone all night while your buddies are getting sleep for the next training day. Those Lt's with laptops have a much better time on duty because they just sit in the office and watch movies all night, vice staring at a wall trying not to fall asleep.
I'm not familiar with the "toughbook", but I would guess that it is a laptop built to take a beating. You don't really need to worry about a computer built to take abuse, as you won't be taking it into the field while you are here. Of course, keep in mind that you may start taking your laptop with you in the future during your flight training or in the fleet... I can't speak on that obviously, I can just say that for TBS purposes you won't be taking your laptop anywhere too extreme.