First 3 Halos: (I'm only omitting Reach and ODST because I haven't played them, also, they are not involved in the Master Chief series)
They were actually witty, well-made, tight shooters. They had good dialogue, a drive, however simple, and a clear enemy that (realistically) became muddier throughout the series as political ties were made.
The Halo games are actually quite good as story-based games. The idea of being a man in a suit with a shield is simple, and elevates you barely above other soldiers, but you know you're unique by effectiveness. I never saw a problem with them.
As far as a sequel is concerned, as long as it has:
1) A reasonable story, not a re-hash of separate/neglected ideas.
2) A whole, complete conclusion that leaves room for no more action from Spartan 117.
3) A real enemy with a minimum of ret-con.
4) If it's a prequel, really consider if that's what the people want, or if it's needed for the series as a whole.
*The following is, undoubtedly my own opinion. Do not confuse this post as a message of fact. If in doubt, after any criminal sentence, slap an "in my opinion" after it. I do understand people can disagree, or shooters aren't everyone's style, but I don't really get the hate.*