Last one to release on PS3 was Black Ops III and who ever put BO3 as the top rank is smoking some weird weed. Overall, play Black Ops I and II, Modern Warfare 2 and 3 and World At War. It's pretty good. Most of the older COD titles had good campaigns and multiplayer.
You can play the game offline, but there are several things you need to do first: Install MW3 via disc or download. If you're using a disc, you'll be prompted to download a 70+GB patch.