First off, this is not a walkthrough. Walkthroughs are one step away from getting someone to play the damn game for you. What follows are tips.
Tip #1 - Sneak and Snipe
|A Ranger, doing it wrong.|
You should give at least one Ranger the Phantom and Conceal abilities so they can stay hidden. These guys will basically sneak around and act as scouts or spotters, while the rest of your squad take up a defensive position somewhere far away. Your Rangers do not attack unless they absolutely have to, as this will break their stealth. Instead, they should keep just near enough to a group of enemies that they (and, thanks to Squadsight, your Snipers) can see them. Your Snipers then pick the aliens off from a distance, and the rest of your team (apart from the Rangers) finish off any that manage to make it close.
This tactic isn't feasible for every mission, especially the timed ones, but it works great for things like supply raids and attacks on facilities, where you can spend as much time as you like scouting and getting into position.
Tip #2 - Not the Boss of ME!
|BURN IT! BURN IT WITH FIRE!|
Talking of rulers - I always hated that Archon one. The reason being, he does that attack where he takes one of your squad high up in the air and drops them the next turn unless you hurt him first. But then, one time I had Dragon Rounds equipped on my Sniper and the Archon ruler was already on fire - he started his attack, picked up one of my squad, but the burning damage hurt him and my soldier was returned safely to earth. I'm not sure if this applies to Viper rounds as well, but I don't see a reason why it shouldn't.
In general, try to keep rulers stunned, for example with axe throws or frost grenades. If your Grenadier has the Heavy Ordnance ability, the grenade in the second slot gets an extra use, so make sure your frost grande goes in there!
Tip #3 - Avatar, Schmavatar (or something)
|Dude, nobody cares...|
Tip #4 - UpgradesTalking of upgrades...
|A Ranger weapon doing it wrong|
Next up is either the Advanced Warfare Centre or the Guerilla Tactics School. Theoretically, it makes sense to build the AWC as early as possible so that your soldiers can have the chance of getting an extra ability each time they're promoted. The faster healing rate when staffed by an engineer is also theoretically useful. However, in practice, I find that it's better to build the GTS and buy the squad size upgrades as soon as humanly possible.
|Well, fuck me. A Ranger doing it right!|
As stated in the first tip, using Rangers and Snipers together is something I've found key. To do this, your Rangers need the Phantom ability at the minimum, and preferably Conceal as well (if you're spotted while hidden, you can go back into stealth later with Conceal). If you use Rangers this way, just remember that they should ideally be in stealth all the time, so it doesn't make sense to choose a load of combat skills for them.
My Snipers are all marksmen (/markswomen? Markspersons?). Long Watch might appear to make sense, but I actually avoid it - if an enemy is that far away, then I prefer to manually choose to shoot. I don't want to risk alerting enemies. Besides, Return Fire is pretty awesome - a free pistol shot against anyone shooting at you, once per turn. This has been enough to finish off enemies, particularly if you researched better pistols. The other important skills for my Snipers are Death from Above (with the extra action it gives, you can reload), Kill Zone and Serial. As I mentioned before, the last two really need expanded magazines to get the most from, but they can be pretty useful even without that.
For Grenadiers, I tend to get the Shredder ability first. Without it, your options for lowering the enemy's armor are pretty limited, especially early in the game. Grenades do the trick, but have limited uses, psionics are out of reach for the early game, other options like the Specialist's Combat Protocol are not that effective except in certain circumstances. Heavy Ordnance is a must-get for me, particularly when you have the Alien Rulers DLC, as you can get an extra use of the frost grenade from it.
Specialists are a little different. Unlike the other classes, the skill choices reflect different roles - medic or hacker, essentially, rather than tweaks to a single role. I usually have one soldier as a medic and one as a hacker, each taking all the skills from their side of the 'tree'.
Tip #5 - Loadout
|Another kind of spider suit|
For a Ranger, a good alternative for the spider suit is the wraith suit. In some missions, you have to sneak inside something - a facility or a vehicle - and hack a chest. The wraith suit means you don't have to go in through the front door, which may be exposed. I once had to hack a chest in the back of a truck and Advent were standing right by the door. I got in by using the wraith ability, walked through the truck and hacked the chest. If I remember right, I lost stealth when I started hacking, but because I was in the back of a truck with the door closed, nobody noticed.. I hit Conceal after and walked right out again. Awesome.