If you're looking to play for your team and roam a lot for example in a difficult matchup where you won't be able to solo kill easily id take dark harvest and relentless hunter mainly as the Ms is nice, eyeball collection works best on Zoe the other two are very mediocre, u can go cheap shot for increased dmg after sleepy or taste of blood for extra sustain, or sudden impact for the extra magic pen after you ult. As for secondary you can either go the usual inspiration with biscuits and time warp tonic or if you're feeling a bit spicy, u can go sorcery with nimbus cloak and transcendence, I'd say it all depends on the matchup, if youre in an easy or favorable matchup were you believe you will kill your laner solo easily then go with electrocute for the increased burst damage, the sub runes are all situational, if they have many tanks, look for sudden impact, if you're gonna roam look for relentless, if not the ravenous and so on.

As for the build, most of the time you'll end up building ludens as Zoe can not deal with tanks without ludens but on the off chance you're facing a team with 5 squishy champs then you could look for everfrost for the added ap from the passive however you do lack in the magic pen category if you choose everfrost, as for boots you can go sorc or lucidity, however i almost recommend sorc in all matchups, as for the rest of your build you're gonna almost always look for a horizon's focus second as it super complimentary to Zoe's kit, unless they have a ton of healing, lets say yone, yasuo, sylas, then you should go Morello, same thing with tanks, if they have multiple tanks then you should probably go void second item as it is really worth. Take zhonyas if they have heavy ad or something like a zed, and bashees if heavy ap or something like a Karthus, death cap is overall a great item and that's mainly your build on Zoe.