Rush a Rod then Deathcap then Rylais or Void staff depending.

I start boots/pots, get two doran's, then rush a rylai's. The slow is stupid useful on her and the enemy team rarely rushes mr early enough to go deathcap first. Not only that, she becomes stupid tanky thanks to the additional health.

I don't see why people go Athene's first. It's nice but after she has two rings, her mana issues clear up almost immediately.

I find her mana issues to be non existant. I play ahri a lot and have more mana issues on her and never rush RoA on her. Double dorans > deathcap/rylais, depending on if you need the health.

Two questions. Do plants apply rylais? Do they proc spell vamp? I've been going for straight ap

Boots, chalice (will upgrade later for CDR), deathcap/rylais (depends how lane is going), then items for bulky AP like abyssal, zhonyas etc. I upgrade boots before finishing my first big item. I also like grabbing a kages early since it will make me money if I just keep it for a while.

She has so much burst you can afford to wait for AP after ROA!

With her crazy ranged harass, Zyra is one of the few champs I feel comfortable taking a Doran's Ring as my first item on. Keeps her mana up, gives her health and AP, helps keep her in lane. First back will pick up boots, another ring, and pots with whatever I have left over. Then rush Death Cap into Giant's Belt into Rylai's into Zhonya's Hourglass.