It depends on the type of game you want to write (e.g. shooter, strategy, cards, puzzle, etc). Really, it's the game that is important and you need to develop this before nailing down the tech and presentation.
Whilst you are learning, everything will take much longer than you think, so you should stick to a simple concept otherwise you might get discouraged and give up. Once you have done a couple of really simple games, aim for something more ambitious.
You could prototype it quickly in Windows using your exisiting experience, e.g. for a puzzle game you might use a Form and buttons instead of graphical icons and just change the text. It doesn't have to look pretty, as long as you are developing the basic game mechanic. Is it fun?!
A lot of concepts will get thrown out during prototyping. You might start again 10 times before you hit on an original idea. There are an awful lot of dross games on the iPhone. You need to distinguish yourself with good gameplay as people get bored of the looks very quickly. Don't just go with the herd.
Once you are ready to move to the iPhone I would definitely use a game library as they supply a lot of useful functionality that would take you ages to implement. You want to spend all of your time on your game, not the support code.
The following look interesting libraries:
