Satin-finish polyurethane (Varathane is a popular brand name) might give you the finish you want. you probably should dull the surface of th existing varnish with fine steel wool before you varnish.
I would use the traditional oil-based Varathane - I haven't been happy with the water-based stuff, which is more like clear house paint. This page (click) has some pretty good pointers.
-Joe-