Fall of reach, First strike, Ghosts of onyx, Last light.
Fall of reach - Tells the origin of the spartan program and features spartans fighting in the human-covant war.
First strike - It essential tells how chief and Johnson got back to earth after the first halo. Features the remaining spartans that survived reach.
Ghosts of onyx - Features the Spartan III's and pretty much every remaining spartan II besides the chief. You also get a little bit of info about halo 2's earth fight.
Last light - Sometime between halo 3-4, this showcases Blue team investigating some "murders" on planet that's doesn't really like the UNSC. Good action/crime novel.
I can't really give you a GOOD reason why... besides they meet your criteria.. All the books are awesome though... All are a worthwhile read.