I agree with the above about "just wanting to be able to do it " thats exactly how I was. I even considered a race school just to do it. There are a lot of you tube clips offering pointers
Schools like the california superbike school don't do body position until level 3 which is about 1k worth of training. However, there is a YouTube vid of them teaching position on the bike
Bloody hell!!! I never realised glad I did it on me own. I spent a lot of time watching clips and getting used to body position first. Practised reverse steering (which has helped me out of an occasional tight corner). Also advised to approach corners in 3rd gear as I think this is considered a "forgiving" gear at this speed. 2nd gear risks a high side as its easier to light the back tyre up and 4th will result in Kangaroo syndrome
Without wanting to go too off-topic here, I thought I should explain that a little better before everyone thinks CSS is a rip off!
What they teach is the mechanics of riding a bike and give you a toolkit that you can us on the road/track to ride quicker and safer.
You have to start at level 1 (everyone does, including professional racers) and progress to level 4. The theory is that there's a lot to learn prior to actually even thinking about position on the bike. Courses are 300 quid+ each, thus around 1000 quid to complete levels 1-3 (3 being where body position is taught).
If you want to simply get your knee down, then it's not the place to go. If you want to improve your riding then I'd certainly recommend it.
For example, you mentioned that you applied the power too early and thus ended up touching down with your knee briefly. One of the things covered in level 1 is throttle control. If you did the course you'd probably find you were on the gas too late, not too early! They teach you to balance the bike right using the throttle just as soon as you've completed the steering input. That's usually way before the apex of a turn.
If you're interested in learning more, I can't recommend Keith Code's 'Twist of the Wrist' books enough. They cover all of the theory about riding bikes on a circuit. In fact they're the course material for each CSS course.
I hope all that didn't come across as partonising. I'm not a great/super quick rider and am by no means an expert. However, I do have a keen interest in becoming one and it sounds like a few on here would like to improve their riding too so I thought I'd share what I'd read/learnt
Oh, and my little boast of the day - the picture above was taken on Corums curve running at about about 10k revs in 4th gear. God, I love that bend
The correct gear very much depends on entry and exit speed and how much you trust your right hand in applying smooth throttle roll on.