Uh...I guess I'll assume it's between the four non-mission pets!

Goldheart's proficiencies are fine, but his equipment is a disaster. While it is all epic/legendary, three out of four boost intelligence and magical damage, while Earth is an entirely physical/strength based element. Lost Grove equips would likely help you a lot, but I don't know if you've gotten that far. If not, there's plenty of Exotic gear on the broker.

Brownie's equipment is fine, assign that last point to either strength or dexterity and he's good to go and deal damage.

Skull needs his element re-attuned. The reason you keep dying is that you have neither a buffer (water) nor a healer (light). Re-assign him to light, as three of his equips are already all magic/intelligence based, swap out the relic for an Evoker/Illusionist/Lightbrighter if you can afford it, and make his proficiencies intelligence, health, agility and move him to the second party slot.

Ah, and a tip to not dying to the chain undead is the bottleneck: only hit the middle one, leaving two weak one-stars on the side, and that way you won't have to deal with three powerful undead at the same time.

Is skull prociency all magic? so I should equip him with magic?

Yes, he needs magical/intelligence boosting gear.

what kind of relic should I get goldheart? Magic or Physical?

He needs physical.

Who should I put first in my party? Brownie or GoldHeart? meaning first slot?

The order should be
GoldHeart, Skull, Brownie.