Champion 3 then. It's sad, but that's all the Champion has to offer you for a long time.
Champion 3 gets you a 20% chance to Crit. Pair that with Barbarian 2 for Reckless attack and you've got a 36% chance of scoring a critical.
Since you've a few, high intensity fights, I suggest sticking with the Barbarian (probably Bear Totem, as you'll be Reckless Attacking a
lot) as it has the highest melee survivability. It also happens to be the most crit-centric, which dovetails nicely.
If you're allowed UA Racial Feats, consider going Half-Elf instead (#Half-Elf Superiority

), as you trade in 1d12 on a crit for 12.8% more chance to crit with Elven Accuracy (for a whopping 48.8% chance
per attack).
To do some maths:
Half-Orc Champion 3/Barbarian 9: 4d12 extra damage on a crit, which occurs 36% of the time. Averaging 1.44d12 extra damage.
Half-Elf Champion 3/Barbarian 9: 3d12 extra damage on a crit, which occurs 48.8% of the time. Averaging 1.464d12 extra damage.
The latter is also better if you're using Great Weapon Master, as a higher chance to crit means a higher chance to cleave.