I haven't tried much of the heavy weapons yet due to ammo shortage.
But I found in other fallouts that a melee/heavy gun build did good. The weak stuff I just killed with melee while bug bad guys got a rocket to the face.
Fallout 4 seems to support the fact that early on you can use all the weapons. Once you start getting the perks then you dmg with one or two types will go up and that's pretty much all you'll use.
And certain creatures are just easier to fight with certain weapons.
Shotguns on ghouls is good. They are pretty fast so with melee its hard to block and you'll get smacked down.
Against mirelurks I found melee to be awesome. They ate slow and its was to block their attacks a hit back.
Raiders....still way easier to just snipe them in the head.
In terms of spreading your perks to thin- I noticed that if you focus on the damage/ toughness perks and ignore the others then the game actually becomes pretty easy even on survival.
I'm 1 or 2 hitting mobs with my bladed tire iron at level 5.