The rocket launcher is the Heavy's primary. The LMG is for support, mainly pinning.
To use a heavy properly you need to use a combination of pinning, shooting, and explosives as the situation demands. They aren't like snipers or assaults where standard shooting is the main point of the class. Trying to hit the enemy with LMG at anything other than point blank is a bad deal because the to-hit is typically ~50% which is just not good enough.
Because the rocket is the heavy's primary, and because standing still lets you use bullet swarm (even if that's not worth the ammo most of the time), you need to treat the heavy as a stationary shooter same as a sniper, but move the heavy up with the squad. Its ok if they lag behind a little, rockets have extra range and suppression can be used even if they move. Then, and this is important, always take the heavy's move last. The heavy has two actions that can be used to save the squad if enemies are left standing at the end of the turn: supression/overwatch and rockets both of which have a low failure rate. Thus, the heavy is a sort of guarantee that if your more accurate squadmates miss, you can blow up or pin down whoever's left.
For heavy builds, a lot of their choices are no brainers. The big choice is really shredder missile versus suppression; suppression lets you kinda-sorta ignore one enemy while shredder missile is effectively a second rocket (against early enemies its still one rocket to kill, against late enemies its a rocket+another shot, so its the same amount of actions to kill as a standard rocket). In theory you can build heavy to add a bunch of extra effects onto suppression (holo-targeting, AOE, and damage) but personally I find that most of the abilities involved in that are mediocre and by the time it all comes together you have better things to do with your time. So I build my heavies as demolitionists; I'm a bit unconventional in that I almost always choose grenadier for cover killing and HEAT grenades.
My favorite build right now is Bulletswarm/Shredder missile/HEAT ammo/Grenadier/Rocketeer, but sometimes I go for suppression and maybe a buff to that.