I've now finished my first playthrough (Expert; will bump it up to Impossible next time around).
This game is flawed but amazing. Breach mode works really well. The significance of order in, different bonuses and penalties for entrances, prioritizing which enemies to focus in Breach based on overall importance, alert status, and distance... it still, at least to me, covers that pre-fight prep thinking you did in XCOM: EU and XCOM2, but just speeds it up and removes a lot of unnecessary problems. Individual turn order generally works well, although it can be really frustrating on evacuation stages with reinforcements popping into the middle of the queue. I think it would address a lot of the irritation here if they just tweaked map layout - put two high-cover hard points on every evacuation zone, so you could have two agents queued up ready to leave on a moment's notice but still providing safe covering fire for the other two as they pulled out.
The changes to HP and healing are also nice. In general, you assume you will take some damage almost every mission (whereas EU / WotC were mostly about lots of prep so you could alpha-strike a pod out of existence before it got a shot off), but it's not as punishing long-term to take that damage as long as you are keeping it within a reasonable level. The game could probably use a second hero with an allied heal ability though; Terminal able to heal every single turn, while other heroes can either heal only themselves or once a mission with medikits, isn't an ideal balance.
The story is... bland. Feels like a lot of missed potential there; one of the big benefits of these hero-characters was that it did give them more control over story and character development, but that seemed to be constrained pretty much to occasional reaction comments during missions and randomized banter between agents.
The strategy layer was fine at what it did, but simply didn't do very much. Limited tech tree, limited agent upgrade options, limited weapon variation, pretty straightforward and not terribly interesting mechanic for controlling anarchy. Nothing explicitly wrong with it, but it left me wishing there was more.
It's also really buggy. Really, really buggy. Two crashes to desktop trying to enter the final mission, getting "stuck" indefinitely on a loading screen once where I had to force-quit the program, one mission where it never actually proceeded to the next stage after the previous was clear and I had to reload, the enemy visibility preview graphic regularly going screwy, nanomedikits replicating in inventory, some unit model issues with units floating several feet off the ground, the wrong ability being used a few times (not the one I selected) or on the wrong hero (not the one I clicked on), some issues with transitions between agents, occasional teleporting enemies when they break in, a number of tooltip errors on gear in the armory, some camera glitches... the list goes on and on. And these are just the bugs I ran into; I've seen some comments from other people with bugs I never saw myself. I love the game anyways, and it was a very pleasant surprise to have it drop into my lap so suddenly, but it really feels like it could have used another month in QA before release.
Expert difficulty was a little lightweight for a long-time series veteran, except for a one escort-the-hostage mission fairly early on that destroyed me twice while I was learning how reinforcements worked. Definitely bumping it up to Impossible next time through.
Strategy thoughts...
Terminal is ridiculously good, best hero I tried. Definitely Pin Down at Field Agent rank, and I think Armor System is best at Senior Agent. Good use of cooperation is critical to getting the most out of her I think.
Blueblood is decent early game; I stuck some Tranq. rounds on him and found that helped a lot with making sure I got enough captures for intel in that early part of the game. By late game he becomes a monster. Definitely Warm Welcome at Field Agent; I'm honestly not sure which I'd prefer at Senior Agent. The better his gear, the better he does. I ran him with Dragon Rounds when I unlocked them, which was really strong, but it's possible that maybe Talon Rounds are mathematically better for him? Not sure.
I ran a lot of Verge. Crowdsource seems promising, but in practice if you don't have Collar he struggles to build up a significant bonus there. And he just doesn't have the necessary action points for Slam, while Network Healing can make him a respectable tank when fights go long. Overall he was... fine, I guess? He had good uses, but I think there are probably agents I didn't try this game that are better. Berserking enemies is also weird behavior; usually they shoot each other (even if one of my agents is closer), but sometimes I've seen them go after civilians or even just move without shooting. I wish it was more intuitive understanding how that worked. Puppeteer is a great once-per-mission ability at max rank, one of the best ones agents get.
Godmother was another one I used a fair amount and found bland. I think you want either two Shotgun heroes in your squad or none - if you're gonna run a Shotgun hero, you're gonna want shotgun weapon upgrades. But if you're getting those upgrades, the other shotgun heroes also become more attractive. I went with Last Stand with her, and then... she never actually activated that ability all game. Flush might have been more useful, although I guess the peace of mind from Last Stand is something. It also might be more useful on Impossible. I also went with Close Combat Specialist, and think I'd have preferred Untouchable.
Zephyr is a really good early- and mid-game agent. Definitely Pressure Point and Moving Target. She does not scale particularly well into the super-late-game, when you could instead by running an agent with an epic weapon and damage-boosting rounds, although she's a decent tank / disruption hero even there.
Cherub underwhelmed me. A very poor substitute for Terminal.
Torque has some nice control potential. I felt like Verge was already covering that spot in my game so I never really gave Torque a fair shake. Next time around, maybe. She might also be able to be a bit of a dodge tank later in the game, because I believe she can potentially have 90 dodge and 2 armor.
Claymore was one who looked really promising, but I just unlocked late enough in the game that I wasn't interested in pushing a fresh hero up when I already had a handful of agents at or near Principal Agent rank.
Did not unlock Shelter, Patchwork, or Axiom. I've heard good things in particular about Patchwork, so I think I'll be working her into my squad early on next game to see what's up.
I think Sacred Coil is probably the most valuable faction to take down; Bubble Grenades and Dragon Rounds are both really useful. The downside there is that I also think Sacred Coil's final mission was one of the trickier parts of the game, so you might not want to do that as your first faction.
Bottom line emotional reaction? This game was amazing. I was having a blast playing it, I think even more than with any previous XCOM game. Which is a pretty high bar for me; I love the series and have played some of the games in it over and over and over. But it's amazing in spite of some pretty major flaws.