Beast barbarian multiclass options

We're playing a campaign in our DMs own world with some possibilities and restrictions, such as magical damage/resistance to non-magical damage is not really a thing so melee fighters could still do damage with non-magical items. Scout and Soulknife Rogue are not allowed. I've seen these two being suggested in other posts. And also I don't know to which level the camplaign will be, but something around 12-14 level.

My character is a half-orc beast barb (16 Str 14 Dex 16 Con 8 Int 12 Wis 8 Cha), that literally turns into werewolf when raging so no weapons in hands and Claws are his main weapon. Right now I'm on 4th level with dual wielder feat for BA attack which DM allowed (no +1 to AC though). I'm thinking about multiclassing into something. My thoughts are:

• Barb 5 (4th attack) - Fighter 4 (Martial Archetype + feat/ASI) - Barb X
• Barb 6 (just for jumping and climbing) - Fighter 4 - Barb X
• Barb 4 - Fighter X
• Barb 4/5 - something else completely

I like the possibilities of second wind and action surge, but not really sure when is the best time to go into fighter stuff. Or any other stuff tbh. And I'm open for any ideas.

As a fighter multiclass I'm thinking to take TWF to add strength modifier to my BA and choosing between battle master (menacing attack, riposte and trip attack) or just champion for better crits.

Any suggestions would be appreciated, thank you!