| "The Pop Piano Book" by Mark Harrison will get you started right away with triads and their inversions. This will give you a great "road map" to master those 88 keys. I am working on the first few chapters, and I've found that if you have some basic knowledge of harmony, it's easy to follow the instructions. The rest of the book is devoted to improvise pop piano parts in different styles (ballad, R & B, gospel etc.). This should help your hand independence. Given the size of the book (enough material for years to come), it's a great value. A CD pack or MIDI download with recordings of all exercises is available on Harrison's website.
For non-pianists, Ross Ramsay's "Piano Essentials" is great to show you the correct fingerings for scales and arpeggios and works great together with Harrison's book.
I've also worked in Jerry Coker's "Jazz Keybord for Non-pianists". Good, but not as inspiring as Harrison's book.
Hope this helps.
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