I use:
4 Assault Rifle/Bolter (the first tech I research)/Fusion Rifle
1 Flamer
1 Grenade Launcher (frag grenades, shifting to plasmas when they become available)
1 Sniper Rifle
1 Medikit in one hand, Machine Pistol/Fusion Pistol in the other
Everybody but the Medic gets a secondary weapon -- Pistols (later Fusion Pistols) for everybody but Flame Guy and Grenade Guy, who get SMGs. I keep free space in everybody's backpack to sling their primary weapon, if they need to. Everybody carries two reloads for their primary weapon and one for their secondary, if possible (although usually there isn't enough Fusion Rifle ammo available; if one of the Fusion Rifle Guys doesn't have any reloads, he'll carry a Bolter in his backpack to switch to if his Fusion Rifle runs dry). Remaining space goes to Grenades, the priority being Gas, Frag (later Fusion), Flashbang, Smoke, and Incendiary. I try to give everybody at least two Gas Grenades (once available) and two Frag/Fusion Grenades, plus a Flashbang and a Smoke Grenade. The Medic's got a lot of free space in his backpack, so he'll carry a bunch of extra Grenades to give to people for reloads, if needed. For the brief period when I've got Stun Rods but not Gas Grenades, a couple guys will carry Stun Rods in their backpacks to switch to when it looks possible to get a prisoner. It would be smart to give one of the other guys a Medikit in case the Medic buys it, but I don't usually bother. Of course, everybody gets the best armor available and advanced armor is a major research priority.
I generally divide into two teams, each consisting of a pair of Riflemen and one of the heavy weapons guys (or girls). Flame Guy's team gets assigned to the really close quarters stuff, while Grenade Guy's team gets sent to more open areas. The Sniper will go with one of the teams until we secure a high-elevation area (a hill or second story window) with decent cover. At that point, I'll leave him there, taking cover during the aliens' turn and sticking his head out during my turn to spot for the main teams and take long range shots at any aliens he spots. If there is no suitable high ground, I'll park him in an area with long sight lines and have him cover that. The Medic also gets assigned to one of the teams at first, but he'll spend most of the battle running back and forth between the two teams (assuming there's a fairly secure rear area) treating anybody who gets injured.
To make it easier to visually see who's supposed to be where, I generally give one of the main teams jungle cammo and the other one desert; the Medic gets urban; and the Sniper gets left with arctic cammo.
The Sniper could be upgraded to a Bolter once the assault teams are equipped, but I like having the 12 TU long range snap shot available from the Sniper Rifle. On the other hand, if your Sniper also has good assault skill, the Bolter would allow him to take part in closer range combat on maps where there aren't good sniping options (like the office tower).
The Medic could carry a two-handed weapon, or a pair of pistols, but I prefer to keep the Medikit in hand so that I don't waste TUs transferring items around. That way, he can do a heal and still have 10 TUs available for movement or a single-shot reaction fire.