What's the best starting items to go with as Leona with the new S3 items?

She has a lot of options, so play around with them and see what you like. Here are my favorites (assuming bonus starting gold and mastery ward and buscuit):
Standard Support-faerie charm, wards, pots
Little Bit Tankier (you'll have to back soon for wards though)- faerie charm, rejuv bead, and a ward. I *think* you can also pick up one pot this way.
Invade- boots, 3 pots
Tanky (haven't tried this yet but it's how Elementz does it and I like the idea)- cloth armor, wards and pots

I'd either go Cloth Armor or the standard Faerie Charm build. Locket of the Iron Solari might actually be a good option to rush now, as it gives both Armor and hp regen which Leona could make use of, and as far as gp10 go, Philo is pretty much the only one you're left with.

Leona needs no items.

I get Rejuv Bead and standard support set up. She doesn't need mana regen, so the extra health regen helps you shrug off some early game harrass.

But that is just me.

boots, 1 ward and 1 pot