I think it's okay for a 13 year old. It's not extremely gory like allot of M rated games are and you don't fight any humans except for the multiplayer, you just fight aliens most of the time.
It doesn't hardly have any bad language in it. There are a few mild curse words in some parts of the games but it's rare.
It's not really violent for an m rated game though there is shooting and killing in it, but the worse gore you ever see is purple and blue blood. The only part about all the halo games that might be questionable is in both halo 1 and 3 there levels where you have to fight zombie type enemies that fall to pieces when they die, but it's nothing compared to what you would see in gears of war or left4dead.
Overall I think it's ok for a 13 year old there's nothing in it that they don't show on tv anyways.
If you are still unsure about it, go on http://www.youtube.com and look for videos of halo gameplay so you can see that it really is a pretty mild game as far as the m rating goes and quite frankly could get away with a T rating.
The only thing to really worry about are what people say and do on xbox live. But It's not the games fault .
Hope that was detailed enough.