I'm thinking of giving my barbarian a level in alchemist. The alchemist's mutagen gives a +4 alchemical bonus to strength for ten minutes, so that stacks with rage! Not to mention the natural armor bonus. That is tempting, but is it worth it overall? I have 11 intelligence, so I should also be able to benefit from extracts.
Right now I'm a level 1 dwarf barbarian with 14 strength, 20 constitution using a dwarven war axe. I definitely have a ton of health, but my attack and damage don't seem that great.
The campaign I'm playing in has a serious tone, moves at a relatively slow pace (few encounters/day), and occurs in a dark setting. As far as narrative, my character would take on alchemy as a quick route to more brute strength (kind of like steroids).
My party is a druid, bard, rogue, and myself. I want my role to primarily be as a bruiser that gets in the thick of enemies so the rogue can sneak attack, and the casters can stay safely at range. This is why I took higher con than strength, but again, my damage is not what it could be.