A LCPL engineer is massive if you can get one. Even without sapper though, four grenades is huge. I'd definitely prioritise a SPEC engy over medic. Medics are nice and a great way to get more bang for your buck with medkits.

Gunners and rockets are both fantastic, but in different ways. A steadied rocket in a good position will make chrysalid pods a breeze. It will annihilate cover and allow you to rip through the outsider pod. On the other hand, caught out in the open or with 3-4 tiles scatter on a rocket shot, your rocketeer is nearly useless. Meanwhile gunners are just a great big bundle of reliability, with great damage, the ability to move and shoot, tonnes of ammo to last through firefights, and suppression (and flush if you're LCPL!).

I don't like infantry as they don't have huge damage early, and can't move and fight as effectively. Assaults are kind of the opposite. Again, LCPL is sosososososososo huge here, if you can get one. Close combat specialist will give you a tonne of power against chrysalids.

Scouts in my mind are superior to snipers this early and on these maps. They're almost required, imo, to deal with overwatch without wasting flashbangs. Holo-targetting can also be a really helpful perk when it comes to overwhelming targets with volume of fire.

Basically I like to prioritise a scout, engy, gunner and assault to level quickly early in most campaigns anyway, as I think they're fantastic early game classes. The fact that 3/4 of them can use shotguns is just another huge factor in their favour.

My ideal team would probably be engy (AP + HE grenades and shotgun), scout (flashbang, whatever, shotgun), assault (flashbang, whatever, shotgun), gunner (medkit, whatever, SAW), medic (medkit, smoke, rifle), and rocketeer (spare normal rocket, whatever, rifle).

That gives you a good amount of healing, great cover destruction / AoE for chrysalids, room for battle scanners if you're worried about seekers, or extra grenades if you want more AoE power, or of course more smoke / flashbangs. The shotguns should ideally be combined with potent cover destruction (grenades and rockets) to kill as many outsiders as possible in the first turn.