My strat is:
2x Assaults (assault rifles to start, upgrade to em rifle and plasma rifle)
2x Heavy (Machine guns, upgrade to heavy lasers and plasma blaster)
3x Sniper (sniper rifles, upgrade to coilgun at some point, but the basic sniper rifle is good throughout the entire game)
1x Grenade Launcher/Stunner
I like to keep a good mix of weaponry, so I use all types. This helps with ammo distribution and making sure I never run out of anything, though UFO:AI is pretty good at keeping ammo available in the store.
Med kits on all, grenades and flashbangs, but to be honest, I never use them. With 3 snipers, I take down most at long range and the assaults are there to help keep the bad guys away from the snipers and heavies. If I get rushed, the Grenadier puts the hurtin on them while the rest pick em off. I also keep at least 2 extra ammo packs for everyone.
For Harvester assaults, I first wait for all the aliens to rush out and pick them off from the sides. Then I send in my assaults in first, put them just before the stairwell... hard to describe, but as you go in through the back of the UFO, you go through the main door, then two more doors. Just after you get into the main body, there are some shelves or something. I put my two assault guys between the shelves and the stair well, my two heavies just this side of the shelves, and snipers behind them in the doors. Then I wait for the the enemy to rush. They usually stop just at my assault guys without firing and without reaction points, depending on the weapon they have, who then pick them off quickly with bursts. If needed, I finish them off with the heavies. Then I send my guys forward to take any enemies who may be hiding in the stairwell. Game over.
I do mix it up a bit on squads, replacing the third sniper for something else, depending on what is available.