Hi JP, the usb N adapter should be backwards compatible, just check the specific details of the one you want and it should list that it would work with both G and N.

For gaming you would want to look at "killer networks" adapters as they are optimized for best gaming performance, not sure if they have usb, if this is too expensive try something like Alfa they have from lower power to high power version for very cheap, this might be overkill but for the price it is great value.
http://www.data-alliance.net/Page.bok?template=alfa-wifi

This higher power should compensate for desktop box blocking some of the signal to the wifi router or remove the weak signal problems you might get with other usb adapters.

This product would be great for gaming and having the wifi inside the desktop if possible the preferred method, http://www.bigfootnetworks.com/killer-xeno-pro/

If they list specs look for something in the 400mw or more tx power range as most desktops stand in odd places with bad signal.

My choice would be airlive n.mini $34 and connect using a network cable to the desktop http://www.airlive.com/product/product_3.php?pdid=pd1286350321930

If you can get something that does multiple streams / channels for wifi then it would be ideal for the HD video streaming. Again as long as it list N and G network in the specs you should be okay.

Hope this helps. Shout if you need more help.