My experience has been,
Very Good:
Plasma (sniper)
Combat Shotgun
Mines
Good:
Combat Rifle (.45, semi-auto)
Hunting Rifle (.50, sniper, wish the damage was more impressive though. 50 cal should do more damage and have rarer ammo)
Assault Rifle (5.56 semi-auto)
Gauss Rifle (ugh, that slow projectile and large hitbox)
Laser Rifle (sniper)
Deliverer
Fat Man (we know it wrecks house, but pure damage isn't everything)
Missile
Grenades
Decent:
10mm Pistol
Laser Gatling
Most 'good' weapons in automatic configuration
Poor:
Pipe Anything
Gamma Gun (maybe workable with rad perks against humans only? why bother)
Gatling Gun
Institute junk (no sniper barrel mods?!)
Magnum (hits hard, but too slow)
Tommy Guns
Flamer
Laser Musket
Syringer
Terrible:
Junk Jet (just for you Odd Donny)
Alien Pistol (this belongs here for being such a disappointment)
Untested (I have high hopes for these, but I'm lame and never got around to trying them yet):
Canon
Railroad Gun
Your mileage may vary and with the right legendary mod even a poor class of weapon can be awesome. I don't have enough experience with melee to really judge the various weapons, but from what I've attempted, the effectiveness of melee drops of pretty quickly... as in the time it takes to swing once, I could have unloaded half a dozen or so rounds for likely more damage per hit. The right selection of perks and playstyle could probably make melee work very well though, but it will never be as quick as chaining VATS headshots at everything in view. I'll probably do a melee focused playthrough eventually though as it just seems like too much fun to pass up.