so only lore that happens from the events of halo 3 and onward...?
well if you really want to get into the lore, you need to read fall of reach, first strike and ghost of onyx and contact harvest (which all happen before halo 3). there is lore in those books that needs to be well known before you can start to understand the story they unfolded after the events of halo 3. on the MCC, make sure you find and watch/view all of the terminals in halo 1 - 3 (the anniversary collections included some really important cutscenes, you can just look up a youtube video with all of them in a supercut). youre also going to want to read the the greg baer forerunner trilogy (cryptum, primordium and silentium).
additionally, 2 other things you might want to watch, the halo legends animated anthology (some of them are great, some of them are horrible, but there are little tid bits of info in the good ones that help flesh out the universe), also halo: forward unto to dawn (movie) if you want to get more familiar with Lasky and co, but those two arent necessary.
from there, its kind of complicated. halo: reach muddles some of the lore with contradictions and other weirdness but mostly keeps things intact (but it definitely retcons a few things, some like to say "clarify" but
), and halo 4 and 5 are important for the lore, but there are also books and comics in between each of those games that are important (which i havent read), and then there is halo wars 1 and 2 (which i havent played).
i havent read anything past the forerunner trilogy, and usually wind up just looking up what happened on youtube whenever a new game releases and i want to catch up on the lore. from what i hear, the newer books and comics arent as good, but some of them have essential lore events that you need to understand in order to keep up with all the changes that have happened in the universe. as it is now, im kind of lost lol, but still mostly understanding whats going on. but because i read most of the material leading up to Halo 4, im way better off than those who never had a good foundation for the lore.
im sure someone else could explain all this better, so dont crucify if im mixing up details
its honestly just easier to watch a youtube video that summarizes everything. heres a couple good ones. the first 13 minute long one covers most everything, but the other two are longer and more detailed if thats what youre looking for