1. You should build the GTS first, and upgrade both officer slots as soon as possible. Set aside your first dollars for the GTS and one of the upgrade stations, do not delay either for one second. Getting the GTS up early allows you to train 2 rookies at a time into classes of your choice, which is one heck of a lot better than gambling rookie lives away in missions for classes you may not want. The officer slot is also unbelievably important - the more time an officer spends with his squadmates, the less time that squad needs infiltrating!!! (along with some minor will/dodge bonuses). Not only this, but officers are better than non-officers at detecting faceless. The first three officers I make go straight into havens. You might think having 2 officer training slots is overkill but it's definitely not overkill - you will want an officer per haven, and you want 2 officers per squad, and you also want highly trained officers, it takes a lot of time to train all these. Why 2 officers per squad? Because usually one of them is training deep into the tree, while the other is active and covering for the training one, and provides the amazing infiltration bonus. If your GTS is not constantly training officers (either new ones, or deeply training existing ones) you are probably doing something wrong.
2. Haven Management - the only correct choice is to station a soldier as the adviser, and preferably an officer. This is because damn faceless steal your supplies every month but if you station a soldier you can sometimes stop it from happening (officer has higher chance of detecting it, as does in general higher ranks). Not only do you prevent supply loss, but the mission itself that hunts them down provides you with various corpses for not that much effort. It's a huge mistake not to use soldier advisers. I would pick an assault or technical per haven, train them to be officer at the lowest possible rank (your higher rank ones should be out fighting), and just have them live in the haven forever. Assaults are good because they can easily flank/one shot enemies, and lightning reflexes is very helpful against the sentry advent. Technicals are good because their rocket is by far the best concealment opener for a one man show, and the flames are good against faceless.
I suggest 1 rebel on Recruiting, and the rest on Intel. Going supplies early is not recommended because the faceless usually eat them up in the early stages of the game before your officers can root them out, and intel is sorely needed to get quality missions. But you do need 1 rebel recruiting which I find is the bare minimum to keep the haven population ticking upwards (yes the soldier adviser helps recruiting but I find you still need 1 rebel to keep the flow going up). Go supply after you liberate a region.
3. Reading missions - under the title of a mission sometimes it says something weird like "intel package" or "liberate: xxxx." I don't have the full list here but those "weird" titles (the ones that aren't self-explanatory) are part of a quest chain to liberate the region. The chain gets harder and harder but the end result will give you a lot of materials to keep moving forward.
4. After winning a mission - check all your operations on the map and in the avenger. Many a time I got so careless after winning a mission that I forgot to start building something, or I forgot to reroute troops to a better mission, thus wasting some days scanning when I should have gotten something else started. Rethink your priorities instead of getting so happy after a successful mission you get sloppy.
5. Liberating regions - it's really really important to liberate regions to secure a steady flow of cash. I made the mistake in my current game of expanding in a "wide" fashion - I have 9 regions contacted, but only 3 are liberated. For one thing having too many contacted regions makes your life a mess of running around every 2 seconds getting new missions, most of them without a good timer because you haven't developed enough rebels in any of the regions. The pace of this game is a very slow one - I think it's preferable to move into and liberate one region at a time, perhaps having one region contacted ahead of your current liberation efforts but don't go too far ahead - there is no need to and you will wind up tying your supplies into resistant comms/power instead of helping keep your troops beefy and successful and securing a steady cash flow for the long term. I know there is a risk of if you keep focusing efforts in one region then advent notices, so that's why you maybe have one "cushion" region to work in if things are too hot, but it's easier than it looks to have too many regions that aren't liberated. Also, the more you focus your efforts in one region (what I mean is spending Avenger scanning time) the better types and durations of missions are available, and often times they can counter the advent strength, and also dark events, that advent is setting up for you.
I've noticed the time on the avatar project is fairly lenient - you don't need to beeline to the blacksite as soon as you find it. This is a Long War. Looking back I would suggest liberating at least 5 regions before making a serious attempt to get to the blacksite. Same with the other objectives. One mistake I made was prioritizing the main objectives so hard that my troops are falling behind in tech. I spent a month with my research on things like studying the codex brain, making a shadow chamber, but those are largely irrelevant (shadow chamber doesn't tell you troop composition like it does in vanilla). My next objective is to hijack a codex, but the enemy hasn't even begun to start using them in their regular troop composition. Lesson learned - no need to rush to the objectives. They are actually pretty difficult/lengthy fights with 40+ aliens in them and take a lot of supplies to build contacts towards, so view the avatar objectives as a supply/gear check rather than something you need to rush into. Build up your troops incrementally gear piece by gear piece. A comfortable early goal is to get your squads to size 6 or 7 with reasonable infiltration times and laser weapons, which can be achieved with officers, suppressors, gear, etc.
Edit: I've found it's OK to expand "wide" in the sense of having many contacted unliberated regions, just put rebels on recruitment instead of intel if you are getting too many missions. Try not to manage missions in more than 3 areas at once; let the resistance build up in other regions you are not actively working in so you have enough rebels to go down the line. But I would again reiterate don't chase the avatar objectives too hard, they don't offer too much in the way of bonus resources and are a significant supply/gear check.
6. Instant research on corpses is still in the game as it was in vanilla; that is once you collect enough corpses of a type, the research becomes instant (upon completing the current research the option will become available). I don't have the exact numbers, they feel pretty high, but the point is try not spend time to research corpses unless you are absolutely going to use the results right away - just wait until you collect enough bodies to get the instant time research which will save you time in the long run. For example I researched faceless corpse right as soon as I got one because I thought they would give me mimic beacons, but they don't in long war 2. I didn't wind up building the results of the faceless research until way way late in the game, so on a restart I just ignored faceless research until it became instant, which was a time saver. It is hard to know what research is good for you since the results are very different than vanilla and I don't have a list of all the tech paths and results, so some testing is inevitable.
7. After your GTS/upgrade, the advanced warfare center is pretty much a must to keep wound times acceptable, so that's where your dollars are going. Following dollars should probably be used to buy up all the recruits in your pool (5 or so), because you will need to aim for a very big list of soldiers in the long run (I started with 3 squads, now am working comfortably with 4 squads, and this is not to mention the soldiers you have in havens, and the ones you replace since they will die, etc).
I don't see a need to rush a proving grounds - it requires quite a bit of time, supply, research, and corpses you don't have to get use out of it. It's an excellent outlet for resources, but you don't have them early on; you should be focusing on getting a wide and stable roster of soldiers on missions.
8. Take time to learn/relearn your weapon/class strengths. For instance did you know that the cannon has a range penalty if you get too close? This is not like it was in vanilla. You will have to unlearn some of your habits to make the most out of your troops. Grenades are hugely watered down - their damage tapers off towards the ends, they have a lower minimum damage, they can't destroy environment very well at all, even plasma grenades only shred 1 armor (you can't even blow up light terrain until you train a level 1 perk with the grenadier, and you can't blow up heavy terrain until you get a MAX level perk - this is in stark contract to vanilla where you did an early simple muton research and everybody got overpowered plasma grenades that ripped all cover and armor to shreds; you have no such luxury in LW2).
Leaving room for more thoughts ^^
Edit:
9. Infiltration bonuses appear to be multiplicative, or at least on some kind of diminishing returns formula. This means the more infiltration reduction you have on a team, the less effective further gear will be. I tested this for instance if you have a 1 man squad, a chameleon suit will reduce infiltration time by 10 hours. But on a 6 man squad where everyone had an advanced suppressor, the difference between one cham suit and no cham suit is only 2 hours. To me the practical takeaway here is don't make cham suits - they are expensive and suck up mobility; just put suppressors on everyone and use officers and you will get plenty of infiltration reduction; the cham suits won't be as effective if you use those basic tactics.
10. psi troops in the 1.0 current version seem very hard to take advantage of. They do not train like in vanilla; they need to get actual combat experience and get a promotion, and THEN you can spend time in the psi lab training them further. They don't train while infiltrating (which begs the question how can you get their skills up if they're always going on missions), and they have a very long training time for the good moves, so these guys seem to be quite the investment...I imagine they are op in the long run (bastion/fortress, and mind control) but they are nowhere near the safe investment they were in vanilla.
11. Do no liberate 16/16 regions, because if you do so advent will launch retaliations on every single haven simultaneously on the map over and over.
