Most, if not all, network adapters are backwards compatible, so if you have one now, it should work with the new router. The only caveat is that the connection speed will be limited to the older technology. For example, a wireless G adapter can work with the wireless N router, but you'll be limited to the 54 Mbps speed of Wireless G.
However, if you need to buy a new adapter, there are several models and styles to choose from. Anything here: http://www.newegg.com/Store/SubCategory.aspx?SubCategor... would work fine with your router. All that matters is your level of experience with the hardware. That is, if you're a novice and/or don't feel like opening the computer case, choose a USB adapter; otherwise, if you want to keep your USB slots open for other peripherals, choose a PCI adapter.
Now, if you want to make things more complicated, take into consideration how big your home is. Will you need wireless connections all over your home? How about outside? If these are concerns you'd like to address, you should specify how much range you desire, as you may also need to get an access point.