Hi,
I often read that EK are not so good, If you think so, I hope this build will change your mind.
EK GWF build
Purpose of the build: Going EK with a GWF is a way to fix one of his weakness : low AC and bad dmg mitigation in general, you will loose in dpr compared to a true GWF Half-Orc Champion but you will be more tanky and useful for your party.
You might experience problems at lvl 3 because you don't have the War caster feat yet. Just use your spells on turn you are not using your weapon for this level.
Race: Human
Starting Attributes: STR 16 / DEX 12 / CON 14 / INT 14 / WIS 10 / CHA 8
Skills: Perception, Athletics, Intimidation, Survival, Arcana
Background: Soldier
Weapon: Two handed sword
Armor: Heavy
Progression
lvl1: GW Fighting Style, Second Wind, GWM feat
lvl2: Action surge (1)
lvl3: Blade Ward, True Strike, Shield, Identify, Thunderwave, Weapon Bond
lvl4: War Caster feat, Alarm*
Lvl5: Extra Attack (1)
lvl6: + 2 STR
lvl7: Gust of wind**, War Magic
lvl8: Misty Step,+2 STR
lvl9: Indomitable (1)
lvl10: Shocking Grasp, Arcane Lock***, Eldritch Strike
lvl11: Continual flame****, Extra Attack(2)
lvl12: +2 CON
lvl13: Counterspell, Leomund's Tiny Hut (replacing *), Indomitable (3)
lvl14: Haste, +2 CON, Dispel magic(replacing **)
lvl15: Remove Curse (replacing ***), Arcane Charge
lvl16: Non detection, +2 CON
lvl17: Magic Circle
lvl18: Improved War Magic
lvl19: Fire Shield, Mordenkainen's Private Sanctum (replacing ****), +2 INT
lvl20: Dimension door, extra Attack(3)
How to manage Spells
Cast as few spells as possible, do not waste your spell slots they are a very limited ressource, use your cantrips in priority. Consider your spells as buffs for your fighter abilities.
1st lvl spell slots are reserved for Shield in priority
2nd lvl spell slots are reserved for Thunderwave and Misty Step
3rd lvl spell slots are reserved for Haste in priority (and an occasional counterspell or dispel)
4th lvl spell slot is reserved for Fire Shield in priority (or an occasional Dimension door)
Cast Haste and Fire Shield asap in dangerous fights. Choose when to use your shield spell wisely (never use it to early in a fight - except on big dangerous hits -).
If at the end of the day you have some spell slots left, just identify/alarm/Leomund's tiny hut/Arcane Lock/Continual flame/Remove curse/Magic circle/Mordenkainen's Private Sanctum before you go to sleep.
AC without any magic item
lvl 1 Chain mail = 16
lvl 3 Chain mail +Shield spell = 21
lvl 4 Splint + Shield spell = 22
lvl 8 Plate +Shield spell = 23
lvl 14 Plate + Haste (+Shield spell) = 20 (25)
How to manage your OA
If the target of your OA is wearing armor use Shocking Grasp. You will have advantage on your roll, if you succeed your target won't be able to use his reaction on your mates who won't have to disengage to flee from it.
If the target of your OA is not wearing armor use a standard attack.
How to manage your HP
Do not ask for heals/or use defensive cds until your HP are low (at higher level let the fire shield proc).
Examples of Combos
Staying Alive (you don't have to draw/use your weapon so it works at lvl 3 without War magic)
Move + Blade Ward + Action surge + Dodge + Shield Spell + Second Wind (+ Arcane Charge lvl15)
Two turns combo
Turn1 : True strike (+ war magic at lvl 7)
Turn2 : Power attack with advantage (+ extra attack at lvl5) + GWM bonus attack if you score a kill or crit
Teleport combo when you need to run Forrest run
Move + Disengage + Action surge (+ Misty step at lvl 8) + Dimension door lvl 20/Dash (+ Haste Attack lvl14) (+ Arcane Charge lvl15)
Party synergies
You work wonders with ranged classes with AOE and/or lasting AOE zones (to experience teleport/thunderwave godness).
Ranger Hunter, Warlocks, Light Cleric, Wizards, Sorcerers, Valor Bards, Land druids are great companions.
That looks pretty good. To be sure, I don't like multiclassing, and will probably not allow it as a DM (it's optional, after all!), nor feats, at least for now. From that point of view, Eldritch Knight is a fairly obvious choice for someone who wants both to fight and wield arcane magic.
By the way, had you used the standard array, the initiat stats could have been Str 16, Dex 13, Con 14, Int 15, Wis 11, Cha 9.
Llenlleawg wrote:
Variant: EK Defender build (based on the EK GWF Build)
Purpose of the build: To tank by maxing your AC and OA stickiness.
Race: Same as above
Starting Abilities: Same as above
weapon: any d8 STR weapon
Armor: Heavy + Shield
Progression same with the following changes:
lvl1: Take defender style instead of GWF style, take Sentinel feat instead of GWM feat
Lvl3: Take Shocking Grasp instead of True strike
lvl10: Take True Strike instead of Shocking Grasp.
How to manage Spells same with the following changes:
4th lvl spell slot is reserved for Fire Shield and Dimension door. Your high AC won't let Fire Shield proc as often as with the EK GWF build.
Cast Haste asap in dangerous fights. Cast fire Shield only against foes with high attack bonus or when you are facing great numbers.
AC without any magic item, this the purpose of this build, AC is your main mitigation value and you can reach the highest AC in the game:
lvl 1 Chain mail +shield + defender = 19
lvl 3 Chain mail +Shield spell + shield + defender = 24
lvl 4 Splint + Shield spell + shield + defender = 25
lvl 8 Plate +Shield spell + shield + defender = 26
lvl 14 Plate + Haste + shield + defender (+Shield spell) = 23 (28)
How to manage your OA changes
Sentinel add the 0 movement and a new trigger to your OAs. Just be careful not to use OA when you are low life, you need your reaction to use shield.
Party synergies
You work wonders with ranged classes with AOE and/or lasting AOE zones (to experience teleport/thunderwave godness).
Ranger Hunter, Warlocks, Light Cleric, Wizards, Sorcerers, Valor Bards, Land druids are great companions. You'll be a decent tank with melee characters though not as efficient as a Dragonborn or a Dwarf Battlemaster.
you need one hand to cast your spell, and you need 2 hand to SWING your two handed weapon, not to hold it. you also have a "free intereaction with your environment" where you could plant your weapon in the ground cast your spell then grab it again.
So you can swing your weapon with 2 hand for your action, then for your bonus action you can HOLD your weapon with one hand, and cast with your newly free hand, then grab your weapon with 2 hand again no need of warcaster for this (still useful for advantage on concentration).
I would switch our your 4th level spell for Banishment, giving you more control over an encounter.
I would probably also switch haste back a notch and use it for close encounters that your party has difficulties to handle, instead
saving up the counterspell slots.
It's not flashy, but you will probably feel good knowing that Fireball did not hit your party for 8d6 per party member because of YOU, freeing up
valuable resources.
Preemptive damage prevention adds up in numbers, too.
Apart from that, most of the things you wrote are the things I detailed in my blog as well, but you beat me to the forum post, mate 
If you follow these steps, you will have a good general idea of how this class should work, it's a very viable skeleton to build your character on.
I actually look forward to seeing this class evolve and adjust as new content is published by WotC and more flavor becomes available to build your characters with.
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