You can likely get a card that will play the games listed for $35-$70 USD, so you wont have to "break the bank" if all you're interested in is COD and Halflife/Halflife2.
You should google and download CPU-Z and run this program. it has an export button on the last tab. If you do this, you can cut/paste the file and post it here. From there, we can give you direct links to cheap, low-budget cards that will offer better performance for more modern gaming.
Also, it would help if you let us know where you live geographically. If you're in the USA, Canada, Europe or elsewhere.