Alright guys. Just finished the campaign. Also played a few MP games on competitive and Firefight.  
 
So the first thing I am not getting is. The playlist. So the idea is that you choose a general playstyle and then the server will through random (strange) modes at you? And you can not just choose one game mode and stick with it. So personally I like big objective based games. (Like Battlefield, which is the other shooter I like to play.) That would be Invasion? But there are subtypes like Invasion Slayer etc. 
 
2nd: Firefight. So there is a firefight option in in the main menu, but this I can not play with random people hum?

I have no idea what the first question is, however you have to go to matchmaking then firefight if you want to play with randoms.

Types like Team Objective give you different game types that are objective based i.e. Multi Flag, 1 Flag, Neutral Assault, etc. Invasion is a three part objective based mode that pits Spartans vs. Elites, and then they switch after a round. It's like Battlefields Rush mode. 
 
FireFight mode in the Main Menu is for your own FF matches without matchmaking. The Matchmaking one is just a ten minute game, or one set (5 waves).

Each playlist has a theme associated with them (i.e Team Slayer will have different Team Deathmatch modes like Swat to choose from). And if you want to play big objective-based modes, choose Big Team Battle -- it has 16 players and modes like CTF, One Bomb but it also has slayer. You can choose Team Objective if you only want objective game-types, but there won't be as many players.

Dear sirs,

Thank you very much for your explanation. I also read through the links. But I just decided, that this has absolutely no appeal to me. When I want to choose exactly what game type i want to play, when I play. And the modes i played so far did not really catched on with me. I was in a Firefight, were everyone had rocket launchers with unlimited ammo. Thats just stupid IMHO. Also that thing with the burning skulls....

Currently I have a ton of games to play so this is agood thing.

" Dear sirs, Thank you very much for your explanation. I also read through the links. But I just decided, that this has absolutely no appeal to me. When I want to choose exactly what game type i want to play, when I play. And the modes i played so far did not really catched on with me. I was in a Firefight, were everyone had rocket launchers with unlimited ammo. Thats just stupid IMHO. Also that thing with the burning skulls.... Currently I have a ton of games to play so this is agood thing. "

I can totally see why it is compelling way of MP for a lot of people. Not for me. The reason for that is, while I only have average capabilities in FPS (for an adult man with a full time job), I do very much enjoy the strategizing part of larger, more (Hollywood-)war like games/modes which also require more specialization and team work. Sneaking up to a guy that operates a AA-gun, so your helicopters can pressure the enemy base etc. Although this game style is totally possible in Halo, if you have friends who are into that as well, games like Battlefield or MAG do a pretty good job at inducing such behavior in players, and then equipping them with a suitable playground. I am not saying this happens all the time, in fact, most of the time these games are as frantically as Halo, but when it happens it is totally awesome. 
 
I am not criticizing Halo for what it does. It is all about allocation of you personal gaming time budget. 
 
PS: ... which will go all to Civ5 anyway ;)

It's pointless to compare Halo and Battlefield series, they have totally different multiplayer and putting those two in one sentense is a good way to start a flame topic/war. 
 
I enjoy both latest console titles of those series.