Warmaster Horus
Explorer
The build that looks strongest to me is Barbarian 5, then Fighter 4, then go back to Barbarian. This assumes Great Weapon Mastery, and you can use the -5/+10 with Reckless Attack on almost every attack (except high-AC targets).
There are lots of reasons for multiclaasing Fighter, but Battle Master is the biggest one. You have extremely high-damage attacks but only an average chance to hit (-5 but with Advantage). Whenever you miss, you can use the Precision Attack maneuver to probably turn it into a hit -- it's like a free attack.
Second wind, Great Weapon Fighting, and (especially) Action Surge are also all very strong and fit perfectly with the Barbarian's role. Level 4 of Fighter is just to stay in long enough to get the stat boost.
After that, Mindless Rage and Feral Instinct are great reasons to come back to Barbarian.
I have it the other way. Barbarian to 4th and Fighter the rest. I want those extra attacks.