I love Halo, but I've always found the lore/stories to be incomprehensible so I'm fine with this.
It was pretty simple before Halo 4, to be honest.
Humans achieve intergalactic travel but meet face to face with cultist aliens. Cultist aliens worship ancient alien technology, which was designed to kill the lovecraftian zombie aliens. And the story of halo is just these 3 races trying to do their thing: Humanity is trying to survive, the Covenant are trying to kill humanity, the Flood is trying to kill everyone. In the games, humanities basic thing doesn't change, they want to survive in all 3 games. The flood, similarly, just tries to kill everyone in all 3 games. Only the Covenant gets a bit complicated once one species breaks away because they're betrayed and realize that the Flood is going to kill everyone if they don't get their heads on straight.
In the books, the main difference is that humanity is depicted much more cynically. For example, the Spartan program wasn't meant to fight aliens, Master Chief's purpose, had they never encountered aliens, would have been to kill other humans who were rebelling against the UNSC's fascistic policies. Also, AI like Cortana also comes with all the standard scifi trope questions concerning artificially created life. Also, if you want to look into it, the Flood themselves can be a trip since their motivation is basically to absorb everyone into it's hive mind, so from it's perspective, it doesn't want to kill anyone but wants to give them eternal life by combining their intelligence into one being.
Then Halo 4 comes in and the forerunners are revealed to be ancient humans, but they're also kind of bastards who ruled the galaxy with an iron fist, and now they're revealed to have actually survived and....well, this was where I dropped off the Halo lore, so you need to ask someone whose up to date with the modern day stuff. I personally just liked Halo lore as it was in the Bungie days and really wish that 343i had gone about it a different way.