AP or tank eve are the most viable options AD eve cost too much gold to build and because it doesnt scale with her ult at all its by far worse in almost every situation.
or
in some cases if you fall behind super early in my opinion skip proto belt its really only good when ahead and trying to gap close when behind you are usually kiting more and wand feel much better later on if you went
and
or
after completing the jungle item and probably follow up with
instead of lich bane.
Eve is a high risky high reward champ the problem is i feel that she sometimes just has too much risk with the reward being pretty lack luster because eve heavily relies on the actives/passive of items to front the damage. This is the reason items like deathcap are lackluster in most cases except for super late game when you need just a little bit more damage.
some other items that are over shadowed in most cases are
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something they changed about eve a long time ago as you know they made her E proc on hit this makes items like nashers and wits end and Botrk pretty strong on eve however nashers is only an item you'd ever really consider if you
A: need to be the split pusher for the team because you are able to able to 1v2/3 the enemy team from getting so far ahead
B: need more burst/sustain damage however this still requires you to still be fed.
Either way you need to be very much ahead to do anything if you are even with the enemy jungle you are behind typically in damage. Most people will probably say stay away from nashers and wits end all together because its a little cheesy and greedy to them considering how squishy she is.
also NEVER BUILD CRIT ON EVE. i tested it a while back her E does not get the damage modifier from crit therefore its useless you usually are not auto attacking enough to ever go crit items. With the other on hit items like lich bane and nashers that do work with her E they instantly becomes better items.
Your E acts as an animation reset so if you can you want your target to be running towards you when you are stalking around if you are too far away you wont get the animation cancel which is why sometimes when you E its feels like you do much less damage either you cancel the auto from being too far away or once in a while you may have an action that eats it so you might use the ability and instantly move away instead of letting it get the auto attack off.
attack speed isnt amazing on eve because like i said you usually are not auto attacking enough but it doesnt mean its useless. one of the reasons nashers is so strong is that eve can utilize the on hit and also get a decent amount of ap and 20% cdr basically acts like a 2nd lich bane in terms of damage.
Playing eve is not like playing most junglers you typically have to know where the enemy team is at all times even with no vision and get into position no matter how risky it is because thats what it takes to push her to her limits this really isnt that hard in solo Q not enough players buy pink wards and if you look at the map objectives and the side minion waves keep track of buff timers and so on you can usually predict a lot of things and path accordingly. Majority of players disrespect eves ability to hook around and flank which is probably her biggest strength because it will draw the front line away from the front to deal with you allowing the rest of your team to collapse. Eve is super easy it play but in reality to make her viable you really need to understand what she is capable of and have very good insight on how a typical team fight will given the comps and state of the game.
TLDR eve is okay but requires a lot of game knowledge and ability to read the map and adjust accordingly. She has a number of build paths but requires a lead to be relevant past the 15 minute mark in most cases. If you don't create leads in the early game expect the later stage of the game to be much more difficult.
PS character control and the ability to dodge skill shots is pretty massive you need to be able to sidestep most skill shots or predict where they are going more on eve than most other champs. Eve is a good champ for learning how to think ahead instead of in the moment which becomes more and more important as you climb the ladder
PSS eve isn't great into or with all team comps and can feels lack luster against deathball comps with heavy cc/disengage/exhaust or mobility typically want to pick her as a counter to immobile comps or with a comp that has a lot of engage tools that like to be scrappy.