Just… Don’t. 99.99999999% of the time it is bad. There is one or two builds that are good but other than that it is trash.

Do Fighter 2 or 3 and rest wizard but have him act like a barbarian. :)

Barbarians biggest feature is rage which completely shuts down spellcasting. In addition barbarians arent known for their out standing intelligence, often the complete opposite so playing as a wizard wont work too well.

I made a barbarian wizard that goes insane if he uses spell rage for to long. I included a balanced homebrew feat of my creation that allows barbarians to cast spells while raging with potential of madness due to channeling raw arcane power while in a deep emotional state. It has disadvantage on concentration checks, and after each turn, they have to succeed on a saving throw against their own spell save DC or lose concentration. Also, everytime they cast a spell while raging, they must succeed against their own spell DC or take a point of madness equal spell level+1 (includes cantrips). You have madness slots equal to half your total spell slots and rages. Once you reach the limit of your madness slots, you gain short term madness. 

For roleplay as well, anytime you gain a madness point, you start acting more rash and emotional about everything.

However, your madness slots don't reset until you take a long rest, and you can continue casting while raging, but once you gained madness points equal to your total spell slots and rages combined, you roll on the abyssal corruption table, as the chaos engulfs you.

Thinking Zealot Barbarian / Blade singing Wizard (if going 3+ levels) (Multi Class most likely waste first turn (Raging Up)

Is there a list of Wizard spell with a Duration but No concentration?

Cast a Spell / Enter Blade Song

Rage / Attack

Wear Studded Leather and can use Blade song and Unarmored Defense for AC (Both work in Light Armor)

I do not like the MAD (unless I can find an Amulet of Health = CON  19)

Quote from Marc_Ducorsky >>

Thinking Zealot Barbarian / Blade singing Wizard (if going 3+ levels) (Multi Class most likely waste first turn (Raging Up)

Is there a list of Wizard spell with a Duration but No concentration?

Cast a Spell / Enter Blade Song

Rage / Attack

Wear Studded Leather and can use Blade song and Unarmored Defense for AC (Both work in Light Armor)

I do not like the MAD (unless I can find an Amulet of Health = CON  19)

Unarmored defense does not work in light armor:  "While you aren’t wearing any armor,  your base Armor Class equals 10 plus your Dexterity and Constitution modifiers. You can use a Shield and still gain this benefit."

Bladesinger or Warmagic would seem to be the way to go here.  

A big issue with Bladesinger is you need a round to turn on Bladesong and then another to turn on Rage.  The best way to go here is probably to use a finesse weapon and get Defensive Duelist.  This is really MAD and requires a dex-based feat, you want to max Dex and Intelligence for AC, and you can't use a shield with bladesong.  You also want to use strength for rage attacks.  I think to make this work you need to run a lowish Constution.  Something like S16 D15 C10 I16, then take defensive dualist for your first feat to make dex 16.  You should probably either use a Rapier, or use whatever other magic d8 weapon you find and hold a Finnesse weapon in the other hand.

Another option is Warmagic.  That gets you the spells and an AC boost (only to one attack) but you can run a lower Intelligence and if needed dexterity.  With that you could go S17 D14 C14 I13, use medium armor and either use a better

Barb/ mage can be done but you may want to flip it in your mind. The good thing about barb is the rage and and unarmored AC boost. The problem is rage and spell casting. The good thing about mages are the spells, the bad is the lack of HPs. So rather than think of a barb that can cast a few spells how about a mage that can rage when injured. Go Barb 2 for the HP and basic barb abilities then go all in as a mage ( either war or bladesinger). You will need to take the tough feat and yes no matter how you do it it will be MAD so you may want to roll for stats and create it when you get some good rolls. 

That's really not a terrible idea to use rage defensively rather than offensively

  Yeah but it’s really a mage first barbarian second so maybe it’s the wrong forum. But this way it’s got the rage as a backup for when injured and after L6 bladesinger ( if you go that route) you still have 2 attacks.

Mage offers nothing to barb first in combat.  Maybe some outside combat utility but nothing in combat

Agreed in terms of melee. But again try flipping it. Barb adds defensive ability to a mage when they are forced into melee. 3 levels of barb gives you all the basic abilities and HP while still leaving you able to get L9 spells. So you are able to defend yourself decently when you have to but are still a full powered ( if a bit later) caster.

but yes, going mostly barb with a few levels of mage doesn’t really do anything for you except maybe add some out of combat utility.

I think its rough with wizards, but it works okay with warlocks. After 2 spells you are a cantrip spammer, being a face smasher instead but with resistance to damage might not be a bad idea. 

Quote from MyDudeicus >>

I think its rough with wizards, but it works okay with warlocks. After 2 spells you are a cantrip spammer, being a face smasher instead but with resistance to damage might not be a bad idea. 

 

 I have a half baked idea for a barb-warlock that uses casts armor of agathys before wading into combat and raging so that the damage shield lasts longer.  It can still eldritch smite in combat while raging, so extra spell slots do not go to waste.  I've not worked out the fine details, but at a high level should work just fine.