As far as Internet access is concerned, a Linux computer will be more happy connecting via an ADSL/router. That gets rid of all the ADSL/Modem problems at a stroke. These days, it's not a huge outlay either.
With regards to your printer, click here for a page I wrote specifically for an Epson R200, but other printers are supported in exactly the same way and I happily print to a Samsung Laser and the R200, without any hassle.
I would encourage you to take a look around our site, as there are other pages devoted to the Linux "newbie" that you may find useful and will give you a better insight into how Linux works. There is also some more advanced stuff on there, but try not to get bogged down with that. It's more for the advanced user and not really necessary to start with.