I know someone who just did this and the cabinets sound almost identical (the 70's wood look). They painted them a high gloss off white with dark green trim. It brightened the kitchen and made it look so much better. And yes, they also got new countertops that also looked to be a granite type color. They also tiles the walls behind the counters with a beige 4X4 diagonal pattern.
As far as the liquid sandpaper, I have used it many times before and it works very well. You might read more about how it works with varnish as I have only used it with painted surfaces. I don't see why it would not work with varnish the same as it penetrated the surface of whatever is on the wood and chemically change it so that paint will adhere (stick) to it.
If you wanted to stain it, you would have to strip the varnish and anything else that is on the wood as stain is designed to penetrate the wood. It will not go through varnish or surfaces treated with liquid sandpaper.
As far as the liquid sandpaper, I have used it many times before and it works very well. You might read more about how it works with varnish as I have only used it with painted surfaces. I don't see why it would not work with varnish the same as it penetrated the surface of whatever is on the wood and chemically change it so that paint will adhere (stick) to it.
If you wanted to stain it, you would have to strip the varnish and anything else that is on the wood as stain is designed to penetrate the wood. It will not go through varnish or surfaces treated with liquid sandpaper.