Buy queens from breeders that have VSH bees, they usually do well. Split each year and let them raise their queen and any queen line that lasts 3 years or over will be the line to raise more queens from. Don't let the colonies die, learn how to tell when they are close to a crash, and when you have one in that condition use a mite treatment. Requeen the colony and continue. Keep the colonies well fed, monitor the varroa populations, and practice good beekeeping.
Bees survive varroa if they have VSH hygienic traits and tolerance for the viruses the mites carry. Cell size has nothing to do with how well they do. If you ever see varroa mites on the adult bees, usually you will have a colony that is close to a crash because the varroa population will be huge.
Original poster, put what state you are in. If we know what part of the country you keep bees our answers to your post will be more accurate. What may work in Florida may not work in Michigan or the Pacific Northwest.