paint or stain over varnished surface

What could be considered, stain or paint, to put on top of a varnished surface? I’m not sure if simply painting over varnish would keep the paint well, I don’t want it peeled off. Basically I have a small piece of veneered furniture, previously it was sanded and varnished, however the result does not look that good, and I simply would like to re-paint/re-stain in order to cover some defects.