I personally tended to bring as many soldiers as possible, and either send them out in squads of 4 (with one watching every possible direction at the end of the turn), or have all the troops proceed across the map in a sort of line so nothing could get past them.
In the beginning I'd equip everyone with autocannons or heavy cannons, and the high explosive and incendiary rounds and engage enemies from long range. (The autocannons would be superior if reaction fire would use autofire, but it never did the original XCom. It did in UFO:TTS, though.) (The armor-piercing rounds also work at shorter ranges without being deadly to the soldiers using them, but need the soldiers to be more accurate)
However, considering Firaxis has been working on gameplay prototypes and testing to see what's fun and what's not, and what works well, for the past 3 years (I read the GameInformer feature in the actual magazine), I'm going to trust that they know what they're doing - and may have reduced the size of the maps and number of enemies to make tactical less prolonged and deadly overall*, or done something to make it so aliens aren't nigh-impossible to shoot while entrance dancing at their UFOs or hiding inside (without high-tech weapons that can remove the walls).
* I tried sending just 6 soldiers on my first mission in the first XCom yesterday or the day before, equipped with mostly autocannons with one heavy cannons, and mostly armor-piercing rounds. Now, it was a night mission, and they had flares, grenades, etc, and much rolled over all the sectoids outside the UFO with no deaths and no injuries. Alas, in the end, one entrance-dancing sectoid was able to shoot every last soldier dead one at a time while they were all crouched 6-12 squares from the entrance aiming their guns at it, despite their ludicrously high reactions and firing skills and despite the prox grenades I tossed at the entrance (which went off, but had no effect on the sectoid) and flares that I put at the entrance too, and regular grenades, which only went off while he was inside, also not harming him. (We had no armor, of course)