...but it may not actually be varnish. It could be shellac. This is readily available and you can easily create that warm woodwork glow again if your wood is in good shape. After stripping countless square feet of trim, doors, etc. I have a few suggestions. Henry in MI should hopefully chime in here, he knows his wood refinishing. Although you have a layer of latex paint on the top, you will be working with lead paints on subsequent layers. Take the precautions you feel you need. I personally keep the dust to a minimum, try to remove the paint in large strips, wet mop the area thoroughly, and avoid grinding the paint up. Thus, you will probably want to stay away from sanding which will be a mess. Depending on the thickness of the paint, a chemical stripper or heat gun will be your best bet. Heat guns work best on many layers of paint over some type of clear coat (varnish, shellac, poly). You want to follow the directions carefully so as to not burn the paint/wood. I found that a heat gun followed by a safer stripper (e.g., citristrip or soygel, with citristrip being moderately cheaper) works well. You will lose the clearcoat, but if it is removable with denatured alcohol, it is shellac, and is readily available either in amber or white. I prefer the amber for lighter woods, it makes them glow. Hopefully you don't have gouged or patched wood. If so, you may need to evaluate whether or not you can recoat over it. You may end up repainting if the wood is in bad shape. In my case, I uncovered beautiful wood with a minimum of dings and light gouges. They add to the character of the old wood IMHO. Try to avoid methylene chloride stripper which, while very effective, contain known carcinogens and are extremely noxious. I used to use them all the time, now I try to avoid them. Stay away from Peel Away products. Peel Away I is lye based and will darken the wood. It is meant for surfaces to be repainted. Peel Away 7 is ineffectual, in all of my test patches, on pretty much all painted surfaces.
Take your time. You won't complete this job quickly. There is no quick fix to paint removal. Be patient and start with something like the top of the mantle. This way to can see the surface and if you decide the work is too much, you can finish off the top and leave the rest painted. Good luck. I've been stripping my hallway for almost a year and am only 3/4 of the way there (although I confess I've been coming back to it while doing other renovations/restorations).