The trick about unarmed is that it's based on Endurance, not Strength. Entirely. So my Legion character had roughly:
3 Str
1 Per
10 End
8 Cha
3 Int
5 Agi
10 Luck
It felt super weird to run a non-brilliant character, not to mention a melee one, but there were plenty of skill points to max Unarmed and Speech pretty early. Then survival, for healing. Along with some crit-enhancing feats, everything went down in a few punches... Way better than I expected. Once I got those crazy mantis-arm "gauntlets" from the Gun Runners, it was pretty much one hit kills on everything but super mutants. Pretty sure those added some reach, too.
And since I had 10 endurance, I could tank a lot of damage. I also took two levels of a DR-increasing perk (not sure if it was added by the More Perks mod or vanilla). I *think* almost all the combat perks I used were vanilla. The only issue was carry capacity, and not quite meeting the STR requirement for power fists (which just made them punch slightly slower). The power fists weren't much better than spiked knuckles anyway, and the mantis gauntlet was much better than either.
I always put a lot into Perception to mark enemies on the compass, but having just 1 PER didn't seem to change that much. Probably because it's easy to just *see* enemies in the desert, particularly if you're used to sniping them with other characters.