Probably the majority will say Infection in my guess
That would really depend upon the map and the number of players, but overall my personal favorite is good old CTF.
SpeedFlag
HogPotato
3 Ball
That’s really a matter of opinion. I like BTB (objective gametypes), with a side of team slayer. Normal slayer, no slayer DMRS.
1 Flag Capture the Flag on an asymmetrical attack/defend type map (Last Resort, Relic, Burial Mounds).
2 Flag CTF
Neutral Bomb
Juggernuat
Juggernaut, Infection and Assault.
In Halo 3, it was infection, but that is horrible in Halo Reach. My favorite in Halo Reach is invasion.
Best gametype? I think Invasion.
But for raw fun, I’d put my vote for anything in Action Sack barring Power Slayer.
Squad Slayer DMRs
Slayer pro.