I've made an unarmed character. You can get a Deathclaw gauntlet schematic fairly early in the game (well, I know that NOW, but not when I started). I tear bad guys apart.
Even without a gauntlet of some sort (brass knuckles, spiked knuckles, power fist) you're pretty well-done. Be sure to take all three Iron Fist perk levels: +15 damage! Also go for 80 in sneak and melee skill. At level 20 pick the Ninja perk. Provided you have 10 Luck, you'll be a crit-ing machine. I just swim right through groups of bad guys.
The only problem I have is if they're armed with a gun: they backpedal while firing. That's why Endurance contributes to Unarmed instead of strength. You take damage if you're unarmed.
Seriously... all manners of attacking are viable. Just depends on what playstyle you want. If you like the whole "raving psychopath berserker" way of fighting you're squared away.
TWO EXCEPTIONS, though: Super Mutant Behemoths and Deathclaws shouldn't be fought in melee or unarmed. Period. Takes too much aid supplies. Just invest a few points in Small Arms or Big Guns, just so you're not completely incompetent with either choice. You'll need a rifle or Fat Man every once in a while.
When all else fails when you're fighting unarmed, backpedal like a madman while dropping bottlecap mines.