Thanks Wizid and Brotrinde. 
Brotrinde: So, if I purchase the TP-Link 551, all I have to do is to shut down the PC, put it in, turn on the PC and Linux will recognize the NIC and configure it? I used to use Red Hat 7 and it took me a week once to install a simple NIC. I don't want to have to screw with this. I know Linux has advance a great deal since then, but I want this to work right off the bat. 
  
But, here's my other approach and maybe some of you network gurus can help with this. 
Rather than put a wireless NIC in her Linux computer, can I just use the wired NIC that already works, by taking a cable from that, to a device that will wirelessly access my router upstairs? 
For instance, Linksys sells an Access Point (Wireless-G Access Point Model WAP546). Can I install this device downstairs, and have it wirelessly connect to my WRT54GS router upstairs, and simply connect her computer to it with a cable? 
If not, is there a wireless device which I can put next to her Linux system downstairs that I can connect via cable to her PC, and which will then connect to the router? 
  
Thanks all!!!