Does "most expensive" here mean "the thing I paid the most for," or "the thing that typically commands the highest price?" These can be quite different, of course.
Either way, I don't have a whole lot of really expensive stuff, I'm sure, and whichever interpretation we choose I'm guessing my most expensive thing would be one of my posters for one of the movies - either my Indiana Jones and the Temple of Doom style "B" one-sheet (offered at a good price from Lucasfilm itself not long ago at all) or my Indiana Jones and the Kingdom of the Crystal Skull bus shelter poster.
My rarest? I have even less idea, but I'm going to go ahead and mention a CD I have. It's a promotional single of "The Raiders March," in a distinctive version done during the Indiana Jones and the Last Crusade sessions. It has the bare minimum in labeling, with no artwork whatsoever. Warner Bros. Records (who released the Last Crusade soundtrack) distributed it to radio stations in 1989 for promotional purposes, and I got it through my best friend, who had a friend who worked at a local station. I have no idea how many copies were pressed and sent out, though I'd guess it's probably in the thousands, so it might not really be all that rare after all.