If you want quite a cheap router that would solve the problem with a computer needed to be on all the time, I would suggest looking at D-Links sortiment. You can find their products
at this
page. Scroll down some and check out the models at "Internet Servers/Firewalls". Look at the DI-804 and the other models. They cost somewhere in the 120$ range.
My family uses on of these products, and they managed to configure it without my help..!
Good luck in setting up your network!
Regards,
Puh