Quick Disclaimer:
I am doing this guide solely because I have been asked for it by enough people that it's worth to post.
I do not intend to Min-Max my Builds further than necessary for my own goals (100% game completion), so please don't expect regular updates if anything gets changed or rebalanced in the future.

At this point in time I have yet to finish the Story mode fully. Right now I'm still missing 7 Cores, so some things might change if they are worth equipping (hope so but won't expect it, the builds already pretty strong and plays perfectly into my Playsyle for Strife).
UPDATE:
I've finished Story, Apocalyptic and 2/3 of the Leviathans Maze. There were some useful/powerful Cores still hiding, so I updated the Guide to match my current Strife Build used for all of apocalyptic Difficulty and later on hopefully successfully clearing the Endless Arena with more than 70k points. :)

Hope this can be of use to others. Have Fun playing, I'm enjoying the Game and Gameply greatly :)

Quick Tips:

• Use all your Cores, irrelevant of the effect, until you can completely fill the whole Tree! Your Stats get increased for all active Slots, with an additional boost for every correctly corresponding core.
  
• Try to fill the 2/3 Star slots with 2/3 Star Cores to get an additional increase in Stats until you can acquire the stronger ones.
  
• Many strong Cores can be bought from Vulgrim, don't be afraid to spend some Souls for them, especially early on to fill 2/3 Star Slots with 2/3 Star Cores. You'll get more Souls than you can spend before long!
  
• There are Cores to increase your Soul acquisition (ex.: Mammon (First Major Boss, therefore easily farmable). Very useful to get a major boost in Souls early on.
  
• Don't be afraid to take a disadvantage on a core, especially once levelled to 2/3 Stars they are by far outweighed by the beneficial effect on them.

The following is the exact arrangement of the Cores:

Start - Nephillim Brute

Abyssal Slot 1 - Moloch
Abyssal Slot 2 - Houndmaster

Left Wing
[Attack - 1 Star] - Grubling
[Wrath - 1 Star] - Tidehunter
[Health - 1 Star] - Duskwing
[Health - Major] - Grinner
[Attack - 2 Star] - Gholen
[Wrath - Major] - Dreadwalker
[Health - 2 Star] - Fallen Husk
[Attack - 3 Star] - Fallen Hound
[Attack - 1 Star] - Feral Tidehunter
[Wrath - 2 Star] - Wraith
[Health - 3 Star] - Tidehunter Shaman
[Attack - Major] - Hollow Fiend
[Wrath - 3 Star] - Legion


Right Wing
[Wrath - 1 Star] - Acid Flea
[Health - 1 Star] - Demonic Magus
[Attack - 1 Star] - Flame Legion
[Wrath - Major] - Blight Cannon
[Health - 2 Star] - Scarab Hulk
[Attack - Major] - Ashworm
[Wrath - 2 Star] - Skeletal Soldier
[Health - 3 Star] - Legion Bomber
[Health - 1 Star] - Corrupted Angel
[Attack - 2 Star] - Armored Legion Champion
[Wrath - 3 Star] - Legion Champion
[Health - Major] - Tormented Gate
[Attack - 3 Star] - Spectral Angel


Bottom Part
[Attack - 1 Star] - Angel Champion
[Health - 1 Star] - Hellhound
[Universal - 3 Star] - Phantom Guard
[Universal - 1 Star] - Grub
[Universal - 2 Star] - Armored Flea
[Universal - 3 Star] - Flea Hulk
[Universal - Major] - Jailer
[Universal - 1 Star] - Fallen One
[Universal - 2 Star] - Broodling
[Universal - 3 Star] - Stormcaller
[Universal - Major] - Leviathan

The following are either the absolutely necessary Cores/Upgrades, or those whose worth by far outweigh any other, therefore wise to farm as soon as possible/early on:

Cores:
Major:
Grinner
Bellial
Hollow Fiend (First Chapter, complete 3 times as it is a guaranteed drop!)
Tormented Gate (Shop!)
Ashworm (Shop!)
Dreadwalker
Jailer (Shop!)
Blight Cannon

Minor:
Spectral Angel
Phantom Guard (Shop!)
Legion
Flea Hulk
Legion Bomber
Tidehunter Shaman
Nephillim Brute
Fallen Hound
(Skeletal Soldier) -> Mainly to counter the 1 Biggest weakness of this build: Wrath Buildup


Upgrades:
Hotheaded
Deadeye
In a Roll
Evade Counter (Both)

Rapid Fire
Evade Combo
Quickstep