Call of Duty 4 is the best game in the series due to the simplicity of mulitplayer, and it's pretty balanced. It was fresh at the time. Although, a lot of people think Call of Duty is "stale" now.
Black Ops 2 is the latest entry in the series. Start there. Mostly because there's a lot of hacking in COD4/WAW right now. No platform is safe from hacking so you might want to start with everyone else today. However, Call of Duty: Ghosts is coming out this November.
Just keep in mind, Black Ops 2 has some glitching (just yesterday, I saw a can in the air during multiplayer), some cheating (don't believe what others tell you, just don't - report them and move on) - if the game freeze at some point, wait it out, and report the person to Treyarch, if it goes beyond 5 minutes of freeze, restart the system and go into a different lobby.
In the killcam, you'll get a freeze if someone is cheating. Like I said, wait it out, then report the person - look for the callsign and do it. And the reason why I tell you don't believe what others tell you when you call them out as a cheater - it's because even though the game is recording in the background, it doesn't really tell you the whole story. If you think the person is cheating, and you recognize the cheat - he probably is. Spawn Trapping is classed as cheating, so whatever you do, just report it.
Other than that, it's the same game, from the same engine.