Your posture is determined by your arm swing. If you swing up and down on a two plane swing then you should stand more upright. If you swing your arms around on a one plane swing then stand more bent over on the balls of your feet.
Putt when 1 or 2 feet off the green with short grass and chip using a loftier club as you get further off the green
The same arm motion that is important in the one plane swing should be used when putting to create a consistent repetitive putting stroke