You need 1,000 Lapis to get the most out of it. With that lapis, you'll want to buy the Premium Mog Cake Recipe, and one extra item synth slot. NOT THE FORGE, NOT THE ABILITY, Just the item synth.
Then, you'll want to run THE HIGHEST level exploration you can. If you can run Maranda Coast or Dwarf Forge, you'll be able to get enough materials to make a premium mog cake bundle in one exploration.
Run Intermediate. You need sacred crystals more than anything, and sacred crystals drop the most in intermediate... and Holy Crystals still drop there too.
Okay, yeah, looking over the event stuff... You basically want to get up to the second island, Zadehl Westersands. That's where the drops start getting to actually be useable for higher cost stuff.
"Moogles wanted to celebrate the moon, so they got together ALL THE CAKES! But a bunch of mean old monsters stole the cakes! GET BACK THE CAKES! The Moogles will pay you!"
Actually if you're just up to the Westersands, it's probably best to buy the Rare Recipe, rather than the premium one. The premium one figures you're getting enough materials from the fourth island to make LOTS
But you DO want another crafting slot. If you only use the default, the MAXIMUM amount of cakes you can make during the event is just under 70,000. Not enough to afford everything.
Still enough to afford some good stuff, but to buy everything, you need around 200,000 cakes. And to afford all the major good buys, you need like 130,000
The biggest recipe also has the biggest material discount, but it's not horribly different from the others. Like... a 10% material discount is all.