Definitely play against CAI. Ignore all other AIs when playing ZK (other than Chickens).
If CAI becomes too easy to beat you can play on larger maps like the one jseah suggested, or you can play against more than one CAI at a time, or you can give the AIs a head-start by staying idle for one or two minutes at the start of the game.
If you can beat CAI there's not much point in playing the single-player missions since they're all basically tutorials to get you to the point where you can beat CAI.
Playing multiplayer is definitely the best way to get better once you've got the rudiments well in hand. Win or lose, it's lots of fun and will expose you to a better variety of gameplay (both allied and opposing) than AI skirmishes will. And don't let anybody give you any crap for being inexperienced or low-skill. Once upon a time they sucked even worse.