Honestly, my best arrangement for early game was 4-6 snipers and the rest flame-guys. First round I would leave them very near the drop-ship but adjust positions to provide overlapping lines of fire to most anwhere the aliens would come, turn reaction fire up, and drop them to a knee.
If there was an obvious egress (a nearby dooway from a big building, or obvious large obsticle for aliens to come around: I would set my flame guys just around the corner from that.
When I had them, I never fired a machine gun and only fired an assault rife once. Grenade launchers are more useful, but lack range and get interfeered with by roofs; so snipers have been better.
Later game, I'm 1 bolter rifle, 1 plasma rifle or grenade launcer with PE grenades (Usually put in the backpack as the stun baton comes out), 2 laser rifles, and 4 snipers.
PS I didn't realize shooting was from the hip. That is only appropriate with grenade launchers and flamethrowers (and old-school shotgunners, but not with a tactical shotgun as is shown there).
PPS Any chance of replacing that with an automatic shotgun like a Pancor Jackhammer or CAWS? Also, a shotgun with a solid or SABOT round, OIW no spread, high damage/penetration, and decent range would make that a fun gun again.