Wireless Adapter For Desktop

Hi,
I've a HP desktop and I need a wireless adapter for desktop to connect it to wireless modem.

Requirement Details:
-My budget is Rs.1000/-.
-the adapter must be supported in both windows and linux(fedora) platform.
-preferred companies: not known

Does the type of wireless adapter to be bought depends on config. of desktop or modem?
Please tell me what factors to watch before buying the device?

Thanks! in advance.