tested on insane difficulty, with ballistic weapons and laser weapon:
Chinook:
2 LMG with medipacks - i always make sure they don't need to reload in the same turn, so i always have at least one reliable source of long-range supression. low priority for armor, until you get the LMG-only-armor. they do not use the medipacks
2 shotgun with C4 - great to finnish of supressed aliens, C4 is mostly for opening UFO doors, but can also be usefull for emergency situations. (throwing C4 into an ufo destroys a ton of loot, but it can save your squad.)
2 sniper, with a rocket launcher and spare rockets in backpack - the rocket launcher is only used for removing cover, or in emergency situations (reaper!). as both weapons are long-range, they don't need armor if you are carefull (although flying armor is usefull once you get it).
2 shield + pistol with stun baton, smoke and flashbang grenades - for scouting, short range supression, and throwing smoke
Shrike:
the same + the following:
1 vehicle
2 assault rifle with medipacks and flying armor - the more mobile scout (compared to shield units with wolf armor as the more durable scout), and my medics. the rifle is a good all-round weapon, i just don't use it on the Chinook because i don't want to remove one of the more specialised troops
every soilder (except the rocket-snipers) carries as many smoke and flashbang grenades as possible without reducing tu, shield+pistol might carry a few more depending on soilder strength/tu (they need at least 2 of both).
If my shield+pistol guys have realy good strength/tu (carrying 3 smoke/flashbang and still having room), i add explosive grenades.
The LMG units are the most important part of my strategy, doing a ton of supression and often enough destroying cover or the alien aimed at. they usually do not use the medipacks, if i need to heal someone they drop it and someone else does the healing.