As far as varnish, I always do a two step process of varnishing, first with a gloss coat (since they are usually more durable), then with the matte coat over it so everything is not shiny and unrealistic, and a matte coat has the added of effect of adding a softness to your color blends.
If properly thinned, I guess you could in theory brush it on, but I have almost always use a rattle can or an airbrush.
I use different things on my mood, but Vallejo makes both a gloss and matte varnsih in a dropper bottle that you thin with distilled water and then I have always airbrushed them on.
Liquid acrylic for non wax floors (Pledge with Future) actually works really well for a thin gloss coat, and seems durable as well. I guess it should be since its made to keep a shine with people walking on it. Many people also make washes out of it by thinning paint with it to make "Magic Wash" as people often call it, as an alternative to "the dip method"
While trying out what products you like, I would suggets checking out "dip" such as Army Painter's Quick Shade. It's not going to win you any Golden Demon Awards, but at the beginning it can make your minis look much better really quick, and is easy. BGG has a good thread here:
Here is a before and after from the post:
and a Dust squad dipped posted by Felkor on BGG that cale out really well, whom I beleive is a member here as well (hope he does not mind me linking to it.)
I have also gone for the super durability of a polyurathane or poly acrylic that you would use on furniture even if I did not "dip", but thinned down, and those minis seem like they could go through a window without chipping, but I am not sure about possible "ambering" of the clear coat over time.
Army Painter has a good matte coat spray can, "Anti Shine Spray", as they call it that I feel is aleast as good as Testor's, but is cheaper by quanitiy you might want to try out, as it give easy consistant result. Vallejo can go on heavy and almost frost sometimes with me.