How do I get from here to Sheet Vinyl?

I want to put sheet vinyl in my kitchen. I've just finished replacing rotted subfloor. I will have cabinets with legs.

Type of plywood or OSB? Can/should I put any other waterproofing underlayment?

(Repost, trying to get pic in preview and be more succinct)

I want to put sheet vinyl in my kitchen. I've just finished replacing rotted subfloor. I will have cabinets with legs.

Type of plywood or OSB? Can/should I put any other waterproofing underlayment?

(Repost, trying to get pic in preview and be more succinct)