No matter what primer you use, you need to degloss the surface of what you have with sandpaper and/or a chemical deglossing agent first. Or better yet remove the varnish/poly layer. Then, especially if you suspect it is an oil-based poly or varnish on the surface, prime with a high quality oil-based alkyd primer such as Benjamin Moore Fresh Start. You can paint either oils or latex vinyls and acrylics over alkyd. You may also use a superbonding latex primer such as MAB Superbond, Benjamin Moore Fresh Start, etc. You should only use latex finishes over this though.