I've always recommended people play Halo in release order, not chronological order. Both for the intentional narrative callbacks and the game design progression.
For a narrative example: on the level The Pillar of Autumn in Halo: Reach, you get contacted by Captain Keyes, who specifically mentions himself and the Pillar of Autumn by name. If you've played release order, you'd (hopefully) recognize his name/voice and be like "CAPTAIN KEYES??". But if you play chronological MCC order, you wouldn't really know who he is or what the ship is at that point.
Another example is Halo Wars 1; The intro cutscene of Arcadia calls out the Pillar of Autumn by name, but the more potent callback is with the Spartan reveal afterward. The music and the visual of a single Spartan, who is shortly joined by (for the first time release wise) multiple Spartans together, just has more gravitas if you'd just played CE/2/3 beforehand.
Game design wise, Halo had a gradual evolution of mechanics from CE to Reach. CE introduces the golden triangle, H2 with boarding/dual wielding, H3 with equipment, Reach for armor abilites/sprint, etc. Playing Reach first then CE after means you have an immediate, harsh regression in overall game feel. Between a single game you lose 10 years of mechanic/sandbox progression.