For guns, I find the hunting rifle to be the best sniper; it has the nicest sight, with a reasonable rate of fire and quick reload.
For cqb, I like A light shining in darkness or the hunting shotgun. I find myself to be really accurate with the .45 pistols (haven't a clue why) and the incredibly high rate of fire on ALSID to make it very effective, especially in close range. I find the riot shotgun to be too ugly, regardless of how effective it is, so I'll take the rugged hunting shotgun instead.
For melee, Gehenna is my favourite, mainly for how effective it is, especially with pyromaniac. Knock-knock is close, as with super slam, in vats, it makes you virtually invincible against deathclaws.
Although I rarely use unarmed, the power fist and spiked knuckles are awesome, even if playing mainly with guns or energy weapons I'll use these early on.
For explosives, I like the 25mm APW, with a high rate of fire, and good range.
Finally, my favourite energy weapon has to be the Q35. With a high critical chance, in vats, it becomes one of the most powerful weapons in the game, despite having a 25 energy weapons skill requirement.
So...
wbu