She gets detected by Pink Wards and Oracles, that alone is enough for -1.
Also, never start without Hunters Machete. That's just terrible.
The first item I always, always build, is Lizard Spirit, and that alone will be faster and better than any item you listed.

Hunter's Machete + Health Potion x5 is arguably the best start for any jungler. Ignite should be a situational summoner spell, only for experienced players who can deal without any estra escapes. Since this is a "noob" guide, Ignite is not a good spell to take.

The standard build is extremely expensive, too expensive for a jungler. I'd recommend swapping out Trinity Force for Liandry's Torment. Athene's Unholy Grail doesn't offer enough damage for Evelynn's burst. Take Deathfire Grasp instead.

Veteran's Scars > Safeguard.

Why is everything in a spoiler? That's not how to write a good guide. Only use spoilers for extra information, or pictures, not the entire guide.

Not many champs farm under the tower unless they are low, or their lane is pushed. Why list how to counter eve? Why not list her weaknesses, and provide solutions to said weaknesses?

Not enough information, simple walls of text. Read the guide I have linked in my signature to see how to use BBCoding.

"To summarize, pure ap Eve needs to snowball while giving her a worse starting point."
You are a goddamm assassin. Your effectifness gets better when you snowball hard. Alltho, your ultimate is a perfect skill for teamfights to get a huge shield, burst the squishys and survive. I dont find a hybrid build bad, but a pure item build makes her a killer not only a "run-around-being-a-annoing-q-spammer".

Very noob guide indeed

"She bypasses any wards undetected, even pink wards."

I stopped and -1'd at that point.

And people ask me why I don't even bother reading past the cheatsheet most times.

^ Ahahah... he did say it's a noob guide.

"She bypasses any wards undetected, even pink wards."

Get the **** out.

The way I am using 'cost-efficient' is in reference to making the most out of the limited gold you get from being the jungler.

Some of the component parts are still quite expensive, even if they are stat-efficient.

Cost efficiency refers to the bang for the buck. For example, Trinity Force costs 3843g, but the added gold value of each stat is 5132g. Eve can use almost all stats very well with the exception of crit chance, which is worth 500g.

http://leagueoflegends.wikia.com/wiki/Trinity_Force

For every expensive item i make sure that the initial components are useful as well. Sheen is a good item on Eve as well as Giant's Belt and Chain Vest.

A cost inefficient build would be something as Infinity Edge. Eve cannot utilize the criticial hit portion of the item very well during team fights, wasting 1k gold just for that. Also that item does not fit into her build path, which is offtank/bruiser.

After Spirit of the Elder Lizard and Trinity Force, Eve is not lacking in damage but more in tankiness. At that stage, team fights are inevitable and Eve usually gets focused. This is perfectly fine, because than the mid and bot laner can do more damage. With a Giant's Belt and her shield, she can often survive.

Atmas's Impaler is very cost efficient with Warmog's, but it is by no means necessary. I'd never build it against ap heavy teams.