If you take barb its more for rage than for unarmored defense.
Extra damage and hit chance plus getting half physical damage is fantastic.
A medium armor will give you a higher AC than unarmored defense, and that does not even take into account that the armor may have other useful bonusses.
If you take the classes as decribed in the initial post you will not get a feat/ASI or a second attack for a long time.
Barbarian rage adds a tiny bit of extra damage but does not give bonus to hit. That comes from reckless attack.
His AC could at least match medium armor with the gear and loadout I detailed above, and I think that the OP wants to play a sneaky, ambush type warrior. My monk / rogue, who has a similar setup except starting from 16 in both Dex and Wis, has much higher AC than my barbarian in medium armor.
The way the OP seems to be planning their build, they would hit level 3 rogue at level 5, giving them 2 bonus actions. This makes up for getting the 2nd attack a few levels late.