Best way to experience Halo MCC (Playing order)

It depends on your priorities:

  • Do you want what makes sense for storytelling purposes?
    • Play the games in release order: Combat Evolved, 2, 3, ODST, Reach, 4.
  • Do you want what makes sense for mechanical evolution?
    • Play the games in release order: Combat Evolved, 2, 3, ODST, Reach, 4 (and maybe stick to the original graphics of 1 and 2 to see the progression of that as well).
  • Do you want to play the games chronologically, and not necessarily be able to understand the significance of plot elements?
    • Play the games in in-universe chronological order: Reach, Combat Evolved, 2 / ODST (see note below), 3, 4

Unfortunately unlike a non-interactive medium like traditional films (choose your own adventure films aside), players are going to be subjected to the actual gameplay mechanics of the games they play (well, duh, I suppose). Especially since videogames are a new medium a lot of gameplay changes have occurred over the decade plus the Bungie (and Halo 4) Halo games span. With film, most viewers are able to suspend their recognition of the obvious technological progress that was made between the original trilogy and the prequel trilogy of Star Wars, but with Halo its more of a buildup of mechanical changes that mostly make each entry better. While there are occasional reversals of new mechanics (ex. the removal of dual wielding), each game tends to be more complex a sandbox, or at least a refined version. With the plot of Reach in particular, it will have more meaning to players who already have experienced the rest of the trilogy; irrespective of mechanical progress.

Answer: I would suggest either playing them in release order, or possibly just sucking it up and playing them as they are re-released (luckily, this will change a few years after this answer is posted). Since games are different than film, I argue that a "machete order" doesn't work nearly as well for them.

Note on Halo 2/ODST: Thanks to some fan efforts its arguably possible to play the missions of each game in chronological order, the missions are as follows:

  1. Halo 2 "Metropolis"
  2. Halo 3: ODST "Prepare to Drop"
  3. Halo 3: ODST "Uplift Reserve"
  4. Halo 3: ODST "ONI Alpha Site"
  5. Halo 3: ODST "Kikowani Station"
  6. Halo 3: ODST "Sadie's Story"
  7. Halo 3: ODST "Data Hive"
  8. Halo 2 "The Arbiter"
  9. Halo 2 "The Oracle"
  10. Halo 3: ODST "Coastal Highway"
  11. After this point resume Halo 2.

There are basically 3 "obvious" orders in which to play the games in Halo: The Master Chief collection on PC, and I would say that all of them are reasonable:

Original release order:

CE, 2, 3, ODST, Reach, 4, 5

Chronological order:

Reach, CE, 2, ODST, 3, 4, 5

Halo 2 and ODST can be interleaved as suggested in the other answer for maximum chronological purity.

Halo MCC on PC release order:

Reach, CE, 2, 3, ODST, 4, 5

I am not aware of any other popular playthrough order that is equivalent to the Star Wars Machete order.

Regarding the story, there are no substantial spoilers for Reach in any of the other games, and no substantial spoilers for other stories in Reach. It is a standalone story for the most part. The end connects to Halo 1, but in a way that I think works well no matter what order you play them in. Similarly, Halo 3: ODST shares some events with Halo 2, and it's probably better to play Halo 2 first or interleave them, but that works in all of those orders.

This is different from Star Wars; the Machete order was created largely because

Revenge of the Sith, and the prequels overall, spoil the big reveal in Empire Strikes Back that Darth Vader is Anakin Skywalker

As for features, the progression was not as linear as you may think. Armor abilities were added in Halo: Reach, completely changed in Halo 4, and completely changed again in Halo 5. Dual wielding is a mechanic that only exists in Halo 2 and 3, and was removed in Halo 3: ODST and later games. Deployable equipment is a mechanic unique to Halo 3. Every game adds and removes guns and vehicles.