Here is a list of of options you should think about for the next camera:
1. Optical zoom, at least minimal (2x - 3x).
Digital zoom: just forget about it. It doesn't exist for you (digital zoom actually is software. You can do same things on your computer)
2. Vewfinder (better optical).
Cameras which have only screen are not good enough for you.
3. Pre-set options: Portrait, Landscape, Sport, etc.
You will be able to take pictures with correct settings if you want to do it fast.
Pre-set options are very useful, but they have very little to do with learning.
4. At least minimal manual control over exposure settings (ISO, Shutter-speed and Apperture). Better if exposure compensation provided.
5. Number of megapixels is not so important for you on this stage, but I wouldn't recommend anything less than 4 megapixels.
i would list pros and cons of all your options.