So, I'm not sure how they classify the anniversary edition as "DLC". I just purchased the standard Master Chief Collection, which is a work in progress. Right now it only contains Halo: Reach and Halo: Combat Evolved. The anniversary edition might have some enhanced graphics and maybe some additional features. I wasn't that concerned about it, because I just wanted the original gameplay.
So, 343 Industries took over the Halo franchise from Bungie. Bungie were the ones that originally developed Halo: Combat Evolved, (which was the first to be released) through to Halo 3, which was an amazing game if you enjoyed the Halo series. They (343 Industries) are working on porting the Halo series over to PC, which is what the Master Chief Collection will eventually contain - Just not all at once. Being an old Halo fanboi, wrapped up in the nostalgia of both the campaigns and online games (these will only have the campaign components) and because I'm not as quick with a controller anymore, I really wanted to get into the series again via PC.
So, it's a judgement call. If you think you'll get into the whole series and don't mind waiting for the other episodes then it's a kind of a decent deal.
They (343 Industries) started populating the collection with Halo: Reach, which is a game they developed. It's a Prequel that directly flows into Halo: Combat Evolved. If you want to understand some of the history/mythos of the game, watch the live action movie, "Halo: The Fall of Reach". It was on Netflix for a time, may still be. I think they also had it on YouTube (with ads). It's a full length production. Because 343 produced "Reach" and Bungie was already out of it by that time, it's not 100% canon, but good enough for rock and roll.
To illustrate Microsoft and Bungie's ad campaigns, here's a group of ads they ran when Halo 3 was released.
https://www.youtube.com/watch?v=40jdpzrpIps The interviews with veterans who served with Master Chief and the "Museum of Humanity" was a brilliant marketing idea to get gamers caught up in the mythos.
The diorama they are referring to in the first segment was actually created by hand and I think it is still at Bungie Studios.
EDIT: OK, so I took a look at the package description and I don't understand their explanation. On one hand they say you can purchase either the separate games as DLC or the Master Chief collection, but the DLC says it requires the Master Chief collection which comes with everything already including the anniversary editions. I just started up my game and it's definitely got the anniversary edition of Combat Evolved on it.