The Burger King experience is interesting. I haven't had any Burger King since being on my carnivore diet. They claim 100% USDA beef, although I am sure it's "Standard" grade. But in any event, it should be pretty benign, and therefore edible. I know they had some controversies regarding their meat years and years ago.
But YES, the Costco beef should be good stuff. I get almost all my meat from Sam's Club, and I believe the fresh meat there is either Prime or Choice (Prime is top tier and will cost more). I usually buy the Choice cuts to save money.
They also have prepackaged Wagyu as well as Grass Fed, and I get both of these as well.
I don't think you will have a problem with Costco meats, at least in the fresh meat sections. I might be more leary of buying a frozen package of burgers, precooked or not, as those would most likely be Select or Standard grade - not that there's anything wrong with that. In the end, meat is meat. The grading has to do with how much marbling is present along with the age of the cow at the time of processing.