Wash down first with TSP and touch up any stain and spray in your varnish.
Why varnish. Hard to work with, has a yellow cast, and does yellow over time. Water based poly is easier, dries clear, does not yellow. Either way, clean well... TSP, Krud Kutter, 50/50 vinegar and water, Dawn dish liquid and warm water. Let dry. Lightly sand with 220 grit sandpaper to remove any gloss and smooth out. Wipe down with a damp cloth. Apply three coats of varnish or poly. Use a foam brush for a smooth finish from a can or you can spray.
Would you consider Danish oil instead of varnish? Danish oil is good for bringing out the rich wood grain, but not recommended for high use furniture (like dining room tables). I used it on an antique side table. Hope this helps. Good luck! https://everydayoldhouse.com/easy-diy-vintage-table-restoration-using-danish-oil-and-restor-a-finish/