I have had a few varnishing disasters. I now avoid the brush-on type of liquid acrylic varnishes, they can lift paint a bit, but that usually only happens if you are heavy handed in your application.

My finishing procedure is as follows, I clean my painting with a damp paper towel and look for spots that are repelling the water, finger prints etc.  I will sometimes mix a very small mount of dish detergent in a spray bottle of water and use that.  A very small amount of the paint may come off on the paper towel so use a light touch. I then let the painting dry.  I place the painting on a flat surface in my work shop, and wear a proper vapor mask.  I like to be able to get all the way around the painting and have a strong light source.  I spray from about 12 inches above the work, keeping my eye low to the board to catch reflecting light and make sure I have covered the whole surface.  You have to find that sweet spot between, just a dusting of varnish, and pools of varnish.  As the spray varnish goes on it looks a little dusty, but in about 30 sec. it usually flattens out to a nice thin finish, so stop every now and then to see if the finish is going to settle out to a nice even gloss.

I also give my spray can a flick towards the floor every now and then to make sure that varnish is not accumulating around the nozzle or my finger tip.  A single free falling drop of varnish can be a huge problem if you are going for that perfect finish.

I should add that I paint with acrylics on board, and like a smooth surface and smooth finished painting.