Starting Items

Doran's Shield Start
Mini Gnar is quite fragile, making this your ideal start item against most top laners.

Cloth Armor Start
This start is safe and reliable against high early level AD threats who will try to cheese you, making use of the fast health regeneration to keep yourself healthy and out of danger.

Doran's Blade Start
You're not completely powerless as Gnar in the early levels, your trading potential with this begins at level 2. Q, AA x2, back off until your Q comes back up. Try to attack minions as often as possible to benefit from the lifesteal, but this could push the wave and put you in danger of an early gank.

Long Sword Start
This is a fair start, viable. Try to damage your opponent whenever possible without taking much damage back, especially minion aggro.

Core

The Black Cleaver
This is a great item for Gnar. It helps him kite, more team utility, and makes him tankier.

Mercury's Treads
These are a good pick up most of the time, CC heavy team or not.
OR
Ninja Tabi
Get these if you're against a opponent with strong basic attacks such as Riven, Tryndamere, Lee, even Nasus sometimes.

Randuin's Omen
Great tank item against attack speed reliant champions, great utility on active.
OR
Sunfire Cape
This item may seem a bit underwhelming compared to Randuin's, but the build path is great and cheaper than Randuin's. I prefer this against burst AD champs who aren't reliant on their attack speed such as Riven, Rengar, etc.

Spirit Visage
When you turn into Mega Gnar, you gain health and get way more health regeneration during the transformation. This item improves your built-in healing and gives you more tank stats.

Thornmail
Gnar only really benefits from about 4 armor items out of all the armor items available, makes it easier to select this obvious one.

Situational

Blade of the Ruined King
This is a great snowball item for Gnar. It synergizes well with his mini form, allowing him to kite and chase. If you think you'll be dueling a lot throughout the match, rush this as your first item. I do not recommend getting this if you're behind, you're better off building tanky.

Maw of Malmortius
If you rushed a Hexdrinker during the early game, finish building it into your 6th item.

Banshee's Veil
Get this item if the enemy team has strong CC and if you didn't get Mercury's Treads, this item works well AP assassins too.

Miscellaneous

Vision Ward
Try to have one placed on the map at all times, buy one whenever you can.
Stealth Ward
Warding will save your life, try to have vision on the gank paths to your lane and watch out for incoming ganks.
Health Potion
why not throw spare gold at health potions, every inch of health counts. Health, vision, and teamwork wins you the game.
Elixir of Iron
This Elixir is for when you're initiating team fights, allows your team to follow up and fight the enemies you're locking down.
Elixir of Ruin
If you find yourself split pushing more often than team fighting, this is better and allows you to one man siege towers. Just be sure to ward when you siege by yourself, you don't want to get caught out.
Elixir of Wrath
Great item for dueling with Gnar, this will always be good for those 1v1s.

Marks

Attack Damage Marks
For last hitting(which can be tedious) and out-trading your lane opponent early on.

Attack Speed Marks
This isn't a bad choice because your Hyper passive is actually quite strong, especially against tanks.

Optimally, I use 5 AD marks and 4 AS marks.

Seals

Flat Armor Seals
For soaking up some early physical damage, you'll definitely want these if you need to start with Cloth Armor.

Scaling Armor Seals
These out-scale Greater Seal of Armor after level 6, if you don't need the immediate armor to save your life until level 6 these would definitely be more optimal.

Glyphs

Flat Magic Resist Glyphs
For soaking up early magic damage, you'll want these if you're against an opponent with constant magic damage output and/or if they have bursty magic damage.

Scaling Magic Resist Glyphs
These out-scale Greater Glyph of Magic Resist after level 6, if you can manage to survive until then without being poked down you should consider using these.

Quintessences

Attack Damage Quintessences
The flat AD these give you are quite good for out-trading early on in the match, especially if you intend to harass with your Boomerang Throw.

Attack Speed Quintessences
I think these are better because they proc your Hyper passive more often which is really strong always.

Soon™