The wireless router does not matter for Linux, for a router you don't need any drivers or something like that, you just need a computer with working wireless to connect to that router
If you want a cheap but working wireless card you can use the TP-Link TL-WN781ND card. It is a PCI Express x1 card available at a lot of webshops and computer stores.
The latest (2013) revision of the card has the Atheros AR9485 chip which is working very well with Mint 15.
If you happen to get an older revision of the card with the AR9285 chip, use the steps posted by me in this forum topic to fix slow or unreliable connection: viewtopic.php?f=53&t=125087#p684629
(Please ignore any other posts in this forum topic, they are about somebody else's atheros problem! The post you need is my post of Friday, February 8 and it should appear on top if you click the link)
You can run "inxi -N" in terminal to see which chip you are having.
Registered Linux User #528502
Feel free to correct me if I'm trying to write in Spanish, French or German.