Myself, I would probably go for Mariokart 64, play about 5 minutes of it, then start an OoT playthrough. Original Smash Bros would be another one worth trying.
Something long rumored and desired is that Nintendo add an N64 online option, similar to the already existing NES and SNES services, but it's unlikely that ever happens. If they were to make an N64 Online option, and assuming it had all the classics and then some, what would be the first game...