Just a small tip from somebody who has made his few first waterstarts recently, something that my instructor told me this summer.
Keep your arms straight (and close to each other) at all cost - you'll get under the water at first, stay calm, just keep them extended and the sail will pull you up eventually.
The reason is you need to keep the sail up us much as possible so it can provide more lift. Same rule as for the beach starts you already know.
I remember I was lying there in the water, with both of my feet on the board, controlling the angle and just waiting for the stronger wind to pull me up (getting under the water few times in the meantime, but I was ready for that).
Great feeling when you waterstart for the first time, keep practising.