You don't need a router. You need a way to connect your pc to the psp and the pc to the internet. So you can connect the PC to the internet using the ethernet port and then use the wireless adapter to connect to the psp. Only certain wireless adapters work with connecting to the psp through adhoc tho. The list is on the Xlink site.
For the last time, it's possible to connect to the internet to play adhoc only games with the psp. Unlike the DS, which uses some proprietary methods, the psp doesn't. Last I heard, the Xlink team was trying to get it to work for DS local wireless play, but I think that was like 2 years ago.