I'm going to assume the main point of the thread is to rank them by gameplay and not by the parts of the story they were tied to.
Long Night of Solace - One of the only campaign space battles in all of Halo, and possibly the only mission in the entire franchise with a non-linear ship shootout (a majority of the pelican fight in the final mission of Halo 4 had a linear fighting path with little deviation or flexibility in terms of free driving movement). I absolutely loved this mission when I first played the campaign back at the launch of Halo Reach, and while it doesn't have the same connection to me anymore it was still a really fun mission to play through on Legendary on multiple occasions.
Lone Wolf - While it was, quite literally, a short lived mission, Lone Wolf had a fun design similar to that of Firefight, where the player is put in an abandoned area surrounded by enemies and their one and only objective is to stay alive. In the case of Lone Wolf there are no timers, but at the same time the health that is scattered around is permanently gone once used, as well as the weapons. This forces the player to have to be strategic with ammo use, their shields, and which combatants they engage / which ones they temporarily avoid. I loved seeing just how long I could stay alive in this mission, and it was a blast to play with friends as well (although playing with friends makes it significantly harder). Not to mention this mission contained one of the #1 most pursued trick jumps in the entire franchise, which, after nearly a decade of experimenting, was achieved just last year on the channel Termacious Trickocity.
Exodus - The most fun I've ever had when it comes to beating the par time on a Halo mission while on Legendary. This mission is full of hidden little tricks and jumps that can be used to skip entire sections of the map. It was also full of constant action, with the exception of the elevator part, making it both enjoyable and interesting in terms of different ways you can play out scenarios. Lastly, Exodus was the mission where I found out about the grenade jetpack launching you could do, which was just satisfying to pull off every time I played the mission, and it sure confused the friends who would run the mission with me.
Tip of the Spear - One of my favorite missions from the campaign in terms of raw gameplay, not to mention a few tricks in design that made it fun to speedrun. It was backed by a pretty action-filled sandbox and a cool skybox design. I'm not placing it at S-tier though because while it was a ton of fun to play, it had quite a number of checkpoint problems and it was also pretty repetitive in terms of objective design.
Pillar of Autumn - Some fun running sections, a challenging and lengthy design, but not too drawn out to become repetitive in my mind. I liked the survival part towards the end, the way the checkpoints were spaced out for legendary gameplay, and the little cannon duck hunt part towards the end. I've also had quite a few fun memories with friends in this mission. Props to Bungie on the amount of stuff hidden away in this mission.
Nightfall - Fun mission, although a bit too easy considering you can literally abandon the rebels part, not to mention you're provided with a sniper with ammo littered everywhere throughout the entire mission. I like the whole 'Night stealth' theme to the mission as we haven't had too many spartan missions based entirely at night in the franchise ( a couple missions in CE, none in H2, 1 in H3, 3 in Reach, none in H4, and 1 in H5). The skybox for this mission was spectacular though in terms of design.
New Alexandria - A somewhat memorable mission in terms of the whole 'flying around and clearing out buildings' design, but personally I did not find it very enjoyable to play and playing it on Legendary was unbelievably annoying. The disco room with the Brute DJ was a nice touch, although the rest of the mission was meh in my opinion.
The Package - A memorable mission in terms of design, with an interesting use of the 'defend the hill' type of objective. Not much to say about this one in terms of negativity. Just an all around decent mission in terms of gameplay.
Winter Contingency - If it weren't for the fact that you can slaughter the Moa and drive a forklift, I would have put this mission in D tier because, while it at least has gameplay (making it better than those in F tier), it was incredibly boring even while playing on Legendary as the Elites were not exactly very difficult to go around and a majority of the enemies were grunts and jackals while the player was provided with plenty of cover.
ONI: Sword Base - There was nothing really incredibly memorable about this mission imo. Drive in a circle, clear out enemies, hit buttons, drive back the way you can, clear out sword base, shoot rockets, done. It just didn't stick out in comparison to the others for me.
Noble Actual - No actual gameplay involved, just one big cutscene.