Do NOT use any enamel based painted or primers. They react with the vinyl based soft plastics and will remain sticky/tacky pretty much forever. I nearly ruined the undead dracolich figure from the D&D Ravenloft board game by priming it with Floquil primer which is quite solvent heavy. Almost a year after I painted it the fig was still tacky to the touch even with multiple coats of varnish (though the harder plastic base was fine). Only thing that finally saved it was I found a forum talking about the issue and somebody suggested a coat of elmers glue, which worked.
Just double check that it's an acrylic based matte varnish and you should be fine.