since you played classical piano, I believe you have some sort of scale or finger-practice book like Hanon or such. Although it can be bit mechanical depends on how you practice, those books are pretty good for warm-up and such, not to mention most of them have both bass and treble clefs. Bach's cello pieces or some two-part invention is also doable and good for your left hand I'd say.
if you are already familiar with theory and ear training - biggest difference between classical and commercial(or jazz) theory is some of the rules on classical music doesn't apply but if you have studied up to contemporary music and such, that's already enough for most of the music out there except some ethnic world music or experimental stuff.
in my opinion, it'd be great if you focus on styles and grooves depends on genre. each genre has several way to play or interpret and different feel of the rhythm along with own vocabulary.
good luck and have fun, welcome to TB
