Unfamiliar with the 77 Varmint model. Does it use tapered barrel? Does it have rear iron sight? These do have an effect on what height of rings you may need to get.
I own a Ruger 77/22 Magnum which has the Ruger ring mounts and with using a Simmons 44Magnum 3-12x44 (44mm front bell) that Ruger's high to extra-high were needed. Don't remember which as its been a number of years.
I've come across a scope ring setup, that has adjustable height built-in with WestHunter rings. They work with scope diameter(s) of 1"/30mm and 34mm, all within the same ring setup, by inserting split plastic rings within the metal rings to take up the scope's tube size. They go from 1.26 at lowest height to 1.50" at tallest height with scope centerline, so they can handle upwards of 56MM of scope bell.
I've used these rings on a couple rifles. They're built quite robust, come in anidized colors besides black and silver. They're made for Weaver or Picatinney rails, so if your Ruger uses dedicated ring mounts, these won't work for you. Found on Amazon and Ebay.