I've finally signed up - here's my second post.
Looking through Left hand advice it's mostly about the Bass/chord. Apologies if this has been said before but here goes:
Turning your fingers through 90 degrees, they fall on Tonic/Dominant side by side (eg D/A) and the major triad in a handy little triangle (eg D/F#/A). Have a look at the Stradella diagram. Also look at how a full octave major scale can be found. Try C as an easy start. The shape is repeatable for any key. Why bother?Well:
1. loads of easy piano music uses single note Tonic/Dominant as a simple left hand and whole generations of blues/rock bass guitar players have made a living out of it. Sounds nice too.
2. John K pointed out the scale shape and I love how he uses it. Not that hard to learn and bits of melody/runs, even whole tunes sound gruntilly wonderful in the bass.