Skirmish is hard because soldiers are equipped randomly, given a weapon even if they suck at this category.
The early game missions are not too hard, though tricky, and how much civilians it's possible to save is a matter of pure luck.
At least, your grunts can shoot straight (especially compared to original X-Com), and while AR snapshots are weak, MG pours a lot and is deadly enough.
So pack MG or two (if you go in two teams). Have a machinegunner (in crouch +RF) covering a long passage, this works well if they can't pop up on top of him.
Always pack at least one GL - indirect fire capability is priceless, especially when an enemy spawns on the roof where it's hard to hit them with anything else. As a bonus, close hits of HE shells occasionally knock out even if they don't kill. Incendiary grenades are fairly lame, but if it can soften up an enemy before it runs into your RF, that's something.
Also, if your scout runs into an alien face-to-face, it's time for indirect fire - get someone else hurl a grenade over a hovel rather than trying to duke it out head-on.
Flamethrowers are awesome, but very circumstantial - short-range and you can't carry anything else. If you get melee-range encounters no matter what, use it with RF all the time and don't bother with trying to rambo anything that doesn't walk into range; otherwise, ditch it until you get the hang of controlling engagement range.
Conversely, a shotgun with slugs is not quite as deadly, but still has good damage, but also decent range and weight allowance for a few grenades, consider giving it to 1-2 point scouts.
Smoke grenades are must-have, both to cover your own ass and to save civilians.
Try to have a fire contact at a longer range - where it's too far for plasma grenades, for plasma pistols it's technically in range, but they'll fire "in that general direction", especially in burst, which is what's going to happen - a rare single hit hurts like hell, but won't kill an armored soldier. And when they shoot in your general direction, they aren't busy massacring civilians instead.
With RF, potshots actually fired are better than uber-bursts that will never come, so select cheap modes - at least you can reduce the enemy's accuracy or soften them up for your turn and if 2 of them RF, they may actually score a kill like this; at very least, soldiers get some practice.
Research laser rifles - the best for long-range sniping; maybe coilguns for medium range sniping / instakill through cover; body armor when available.