On classes:
I think the ranger is a decent early finisher with the sword. But once you get further into the tree the sword gets totally outplayed by the shotgun. Which is quite early on. I kind of see though that the ranger is your maximum damage unit, which is useful for really powerful enemies. So it is always worth having one on your team.
The Grenadier is the most versatile class, and always worth having at least 1 if not 2 in your squad. They are also the best at destroying cover, which is crucial.
The specialist is an interesting class. To begin with I made one medic and one hacker. Now I am approaching the end (I hope – unless something terrible happens again like my last mission), I think the medic is actually inferior in almost every way. The combat hacker, in contrast, is actually very useful. Not so much for the hacking, although if you had a decent tech score then it would make hacks more viable. I just think that usually the negative consequence of a failed hack is usually too bad a thing to contemplate. Especially on timed missions. Last failed hack attempt I had spawned a heavy mech, a regular mech, and a heavy stun lancer. And that is no joke. I was trying to get some extra intel at an 80% chance. But honestly it really wasn’t worth that 20% chance. I barely made it out alive managing to evac the VIP with turn to remain and an unconscious soldier in tow. But combat protocol, although it doesn’t do that much damage, it does ignore armour and properly upgraded is decent against armoured units and also useful at finishing.
The sharpshooter I think is probably the worst class, aside from the medic. They do get a decent amount of kills, and kill zone is a decent perk when you have a swarm of enemies and combined with an upgraded clip size and scope. The reduced power of squadsight and higher number of hitpoints though make snipers less devastating than they were in EU/EW.
Psionics is the most powerful. They allow you to control a battlefield. Stasis is hands down the best perk. It basically reduces enemy effectiveness by 33% for most pods. The others are pretty decent as well.
I think the squad makeup of:
2 psi ops
1 grenadier
1 ranger
1 specialist
1 sharp shooter
Is pretty best for most missions. Sharshooters are good if you can get them a good vantage point up high. But that’s not always possible on all maps. On black sites though you might want to sub in a grenadier.
On items:
Assuming the above is correct, then I think you should can the medic. Their best ability is probably revive for when stun lancers knock you unconscious. So maybe worth taking on missions with a timer. If you don’t though, then you should really take a medikit for at least 2 members of the squad. That means only one item slot with predator armour. I think using both slots on the sniper and 1 each on the grenadiers is probably best. But not sold either way.
On radio relays:
I think you need to place these strategically aside from the 3 you can usually place in your starting area. It depends on how much intel you have to spare. But intel costs double without a radio nearby and the cost goes up with each mast, so something to bear in mind. This is more of a problem on classic difficulty as you have fewer jumps you can make in a web, instead being forced to use a more linier route to your goal. I think on normal you can jump from the US to western Europe no problem. You cant on classic, you have to go through asia. So to reach western Europe with no masts would cost you a huge amount of intel. And intel is better spent in the black market.
On building:
This is a tricky one. I think it is a viable route to try and max out your engineers and plunge straight for the nearest power core, assigning multiple engineers to each excavation and rushing the power plant once complete. That leaves you enough money to buy one resistance com and the guerrilla tactics centre, which should be built off the bat. The workshop should be built on the third tier down (middle column) just about your power cores (assuming thats where they are). That gives your gremlins access to 4 rooms, which is plenty. Top row should be AWC/Psionics, Guerrilla warfare and Proving grounds (IMO).
On combat:
There is a marked difference on classic. Either that or I was just lucky on normal. But enemy abilities activate much more frequently. Stun lancers used to be an annoyance. On classic they can really screw you over knocking your troops unconscious about 25% of the time. Then you have to carry them, and that basically removes 2 soldiers from your squad. But can be satisfying if you somehow manage to evac all your troops.
On research:
Top priority should be magnetic weapons and plate armour. Take the armour first if you can. An extra item really helps. Good utility items include the mimic beacon (faceless autopsy), which basically gives you a free turn if thrown correctly. The flashbang can also help early on in a pinch. You can wait on the skulljack. Its more difficult, but certainly doable later on.
On the black site:
I waited until I had predator gear and magnetic weapons for the first black site, and my counter is fine. So I don’t really see a reason to deviate from this. You can get a 50%+ to research time on either magnetic or plate armour from the black market, so try for that if you can.
On missions:
IMO the most important are supply line missions. These net you a huge amount of gear and corpses and are not to be missed out on.