In a nutshell...
Team Deathmatch is, if nothing else, good for getting a lot of general combat training in a relatively small amount of time - you don't have a huge number of objectives to worry about, so you can focus on getting your aiming down, leading your shots, and all that sort of thing.
Arena is similar to TDM, but a step up - the games are smaller, and there are so few available respawns per match that every death counts; in addition, the general skill level is increased considerably with significantly smaller map that place more emphasis on direct confrontation than skiing.
Rabbit is a good way to practice flag running and such - in rabbit games there is a single flag; the goal of the mode is to hold on to the flag as long as possible, while everyone else in the server tries to kill you. Players that do not have the flag are considered to all be on a single team, making it vital that you be able to run like hell.
Those are my favorite game modes. CTF ranks in there somewhere, but I tend to be focused around killing folks enough that I gravitate to other modes unless I'm playing with someone.
Hit me up on Steam next time you're about to play.
Just finished a few games with @Twiliscael, was some good times. x)
I think I did okay.