Do you have just one computer connected to the internet? If so, why would you want a wireless printer? If you have more than one computer you must have a router. Is the second computer connected to the router with a cable? If it's not connected with a cable you must have a wireless router. I have a wireless printer that's connected to my router with a cat 5 cable. Brother told me that it's a more stable connection that way and the printer is only about 3 feet from the router so I connected with a cable and can print from my laptop in a different room.

To answer your specific question, I'd shop mainly by price. I don't see investing too much in a network adapter for an older computer. You'll want a USB adapter. I don't know how you feel about this or what you might have done, but it might be worth the effort to poke around a bit. I'd check with HP for the latest, greatest driver and install that. If that doesn't help, I'd delete the network card in Device Manager, reboot, let Windows reinstall it, and see what that does. The computer does use a mini card so you don't have to replace the motherboard. I can't see it being cost effective unless you can find a used one somewhere and have the ability to replace it yourself.

if you were looking on craigslist don't give up hope because there are definitely some good ones out there, I have been lucky and got great deals, you definitely want to be able to try them out and make sure they run properly and that the copy of windows on them is legit, try going to windows update site with it and have it scan the pc to see if it has any problems, if it is not a legit copy you may find out by doing the windows updates trial. I also always go to belarc.com and let it run on the pc and then view the info it gives about the pc to make sure what they are telling you is really what is in that pc. I also go to the event viewer and look for red flags and to device manager and look for yellow flags.

Just don't try doing this with a regular usb cable!! I prefer to use a usb flash thumb drive to move them if you are not networking them. I never cared much for the usb transfer cables.