Newbie needs help. If I buy a notebook do I also have to have a tower?

I am thinking of buying a notebook. The clerk at CompUSA told me that if I wanted to be able to use the notebook anywhere in the house I would need a wireless router. He explained that the notebook has the capability of getting a signal at let's say a Starbucks, however, I may not have a signal in my house.

That much made sense. Then he said I would also have to load the software for the wireless router on my old tower. I would then plug my DSL line into the router and I would have the ability to use the computer in the bedroom, kitchen or living room.

I was shocked that people that only had a notebook, also had to buy a tower to have the mobility within their own home. I would have thought I could load the wireless router's software in my notebook. Am I incorrect? Do I really need to have a tower as well?

Your guidance is appreciated.
k