Did you test it with the actual game online on your computer? Or just the website "www.canIrunit.com" type testing? If you did the website... sorry to say, but you still won't have a good experience. It WILL work, you just won't have fun.
Black ops can be purchased in a store but you will still be required to download steam to play the multiplayer. You can download the map pack through Steam, only through PayPal I believe so it's limited. They are NOT free as we were "told". Also, you don't need to download the map packs. Like I said, you can find lots of servers without them. Not a lot of servers have them in rotation.