If you really know NOTHING about Pcs then Freespire is probably not a good choice of Linux OS for you . Ubuntu would be much better.
As for will it plug directly into your internet connection, it depends on how you connect to teh internet. If you have a router then I would say it most probably will as long as the mother board has an on board network card. It won't be wireless although it shouldn't cost more than 15 quid to make it wireless (obviously dependant on your router being wireless)./
If you just use a USB modem then it depends on teh make and model of modem. Linux is different to Windows and some/most manufacturers don't release drivers for their modems to work under Linux. You do however have many enthusiasts who write them for you. Most are now supported but we would have to check to be sure.