If you have good spray equipment and are skilled with it, I believe you will get a superior finish by spraying.
I really have to wonder why you would varnish over paint... I would use a water based poly and spray it on. An oil based varnish is going to change the perceived color of the paint and might look pretty bad, especially if the color is light.
Good luck.
Woodchip
unfinished furniture store.
about applying the paint (latex). Is it better to spray or brush? The furniture is currently in my garage, so I do not have to worry about paint getting on other items.