Tough, I have two favorite Connery's, same for Brosnan but I also like OHMSS.
If I only had 3 I'd go with
The Spy Who Loved Me
I omit the Daniel Craig movies cause those are good spy movies that riff on Bourne and not really cinematic Bond movies. Even when other Bond movies were adapting other cinema styles to the franchise as noted earlier the series still retained a strong sense of Bond style that the moviegoer had come to know. The Daniel Craig Bonds are a pale reflection of that which came before.