Joe,
Why start with books if you don't want to read music?
I started late on the piano and started with music books but soon switched to online lessons. I particularly like Willie Myette who has a couple of hundred free lesson tasters on Utube. He is a very (very very) good player and a very good teacher too. His stuff covers everything from basics, theory, gospel, jazz, latin, cocktail, blues. Like yourself he is not interested in teaching the classical 'read everything' way.
I started on trumpet the classical route. I could not play a note without a piece of paper in front of me. I then switched to sax the jazz route. I found my reading actually got worse as I found myself memorising everything after a few goes through the head.
As far as Piano goes, if you are considering Jazz, then it may be wise to learn to play treble clef melodies (if you cant already) as this opens up Real Book standards.
One thing I learnt the hard way. Don't confine yourself only to 'straight chords' by which I mean the standard chord and the inversions of, but also add in notes and spread the chord across the keyboard. The sooner you do this the sooner your playing will sound mature. Its a brain wiring thing.
This is called 'voicing'. Voicing and voice leading are very important topics and a good (non classical) teacher can help you with this.
Zero