As someone who is definitely newish to the sport compared to everyone else around here, I went through this at the start of the Aussie summer season just been (October last year). So hopefully I can give you some good info on this. This is what worked for me.
I'm left foot forward, so the ski tip goes on the left side of the rope. Usual drill, knees to chest and elbows outside of knees. Before rope goes tight and if you have both feet in to start, ski can be at 10 or 11 o'clock (1 or 2 for RFF) to help keep your balance whilst floating in the water. Sometimes if you find yourself tipping to one side while floating when both feet are in (if you're a 2 foot starter), I find I just tip my head back in the water and look at the sky for a couple of seconds and that settles it.
When you tell the driver to go, forget about the rope not having a long V. Put the ski to 11 o'clock (or 1). As you start to move, push forward with the ball of your front foot in the direction of the boat. This will straighten the ski for you. MAKE SURE you don't push your whole foot forward (common with trying to stand up too early) as that will make the ski push against the water, and you'll be pushing a wall. That pressure will also make the handle get ripped of your hands.
So, while pushing the ball of your foot forward, simultaneously bring your back foot under you. This action should subconsciously make your back heel come up which combined with pushing the ball of your front foot forward will help the ski flatten out and get on top of the water. Be sure to keep your back knee in against your front knee, otherwise you may lose your balance and it may also catch the water and bring you down. Then, just stand up as usual once you're on top of the water.
I realise I've just exposed myself as the noob I am, but I don't care. This is a great sport and I am addicted. Haha. But, these are the tips that the great people at my club gave me, and they got me from not being able to get out of the water at all, to deep water long V and then short V within a couple of short months, and I was 113kgs then. Since then, I've probably missed 2 starts in the last 50. So if I can do it mate, you can. Get yourself some Radar Vice gloves too, it will help with learning.
Best of luck.