Hey guys I need some help improving my barb. http://us.battle.net/d3/en/profile/kibs-1603/hero/62347424

I want to do higher level rifts but I get one shotted and my damage doesn't seem that great.

How do people get their damage to 1mil and how can I get more tankier and still produce good damage?

Get more ancient gear, especially weapons, get more paragon levels, you need crit chance and dmg on both rings, amulet, crit dmg on gloves.

Just keep farming, and farming.. and farming.

What item should I prioritize spending my blood shards on?

Whatever item that seems to have the lowest stats of their range. It's really a higher focus on rerolling stats on your items since I can see you haven't changed many of them.
Bracers cold dmg to physical is a good start, would give you a nice dmg boost. Get rid of area dmg on gloves for crit dmg.
Take some time to focus on leveling up a couple legendary gems as well, especially bane of the trapped which would be your best one at rank 25. Assuming you can do T6 easily, farm trial keys and do the lowest grift that still guarantees 100% upgrading chance, rinse, repeat.

your barb needs meat. with a name like vegan of course he's not going to do any damage. he's a vegetable!

on the subject though...

you are lacking alot of crit hit chance and crit hit damage on your helm, amulet, gloves, and rings.....

Thanks for the tips guys!

What about when it comes to toughness. Do I need to raise my resist up more? Is resist important or armor?

Craft a Reaper's Wraps

Don't have the recipe for it.

Malthael drops it, just redo the quest and he should drop it. The general ratio for armor:resists is 10:1 so you should have 1,000 armor for every 100 resist so change your stats accordingly.

Is this doable in adventure mode? I got plvled and I am still only in A1 in campaign mode.

Or do I have to run through A1-5 all the way to Malthael?