Best wireless adapters for ~$20 range? Also network name issues?

[Daenar]

Not including shipping, what's a really good reliable wireless adapter in the $20 range? Right now, I'm aiming towards this Rosewill one.
http://www.newegg.com/Product/Product.aspx?Item=33-166-056&SortField=1&SummaryType=0&Pagesize=10&PurchaseMark=&SelectedRating=-1&VideoOnlyMark=False&VendorMark=&IsFeedbackTab=true&Page=2#scrollFullInfo
Also there's the TP-Link that alot of people seem to like:
http://www.newegg.com/Product/Product.aspx?Item=N82E16833704045

Helping me pick one of these or offering a better suggestion would be appreciated. I want to be able to play games and browse the internet. Hopefully it's good for streaming too, but it's not as necessary. My desktop should have PCIe/PCI available. USB is also fine and I don't really care if it's big or small.

Also, I recently built a new computer and installed the LAN drivers on the motherboard. When I put a wired connection, the name of the connection shows the name "Network", but on any other computer, the name is different (my address). Should I have done something else?

 

[RealBeast]

I've used dozens of that TP-Link model and recommend it highly. I would use USB over an internal card now, less hassle, easy install, and better quality.

No, in the system tray (lower right corner) the icon will say Network and if you have it, it will also say Internet access. Other computers will use your computer's name, given when you install the OS.

edit: if you want the best speed for your wireless, in your router set the mode to N only (also known as 300 or 150 only in some routers), use WPA2 security (personal) and AES encryption. That will allow full N speeds and not allow old G devices to attach and slow your connection.