IPhone:Open-gl to start with..

Quartz 2D is not applicable for game development IMHO. It is a software rendering API. It won't give you realtime rendering speed. It's good for drawing charts or vector text with shadows, or for blending several images together. Just not for games. Unless you want to make a game where few images are moving against a monochrome background and even in that case I doubt it will be really smooth on older devices. I've seen some games obviously coded with Quartz. A pitiful sight.

Sooner or later you'll end up using Open GL ES or a game framework build on top of it. I recommend you to check cocos2D, SIO2 engine, or examples from SDK. With careful programming it is possible to make an Open GL ES game with parallax scrolling and relatively small amount of objects work at 60 FPS even on 2nd gen devices. Tiny Wings is an example of such game. And maintaining stable 30 FPS is not a problem at all.

Core Graphics

For this, I'd first recommend reading the Quartz 2D Programming Guide. It's the best set of documentation you'll find out there on the subject. Next, I'd read through some of the questions here tagged core-graphics, quartz-2d, or quartz-graphics. There are some great source code examples in the answers to those questions.

OpenGL ES

There are many "getting started with OpenGL ES" questions here, with links to many resources. These include:

• Books on OpenGL ES targeted towards the iPhone
• Learning OpenGL ES 1.x
• What do I have to learn to get done with a 3D racing game for the iPhone? What Tools do I need?
• Want to display a 3D model on the iPhone: how to get started?

I personally recommend the book "Mobile 3D Graphics: with OpenGL ES and M3G", as well as the "OpenGL ES Programming Guide for iPhone OS". My application Molecules is open source and it uses OpenGL ES. Finally, Jeff LaMarche has a great tutorial series on OpenGL ES.

Core Animation

By Quartz Core, you probably mean Core Animation. Again, I'd start with Apple's Core Animation Programming Guide, then take a look at the code examples you can find here under the various core-animation tagged questions. Beyond that, Bill Dudney's Core Animation for Mac OS X and the iPhone book is a very good introduction, and Marcus Zarra and Matt Long's Core Animation book looks to go into more detail on the subject.