The word I see most often for this kind of person is "collector." That's not very specific, since the collector could be collecting anything, not necessarily fine decor/furniture. If you want to emphasize that someone really appreciates nice things, you could call him/her an "aesthete," which the OED defines as "A person who professes a special or superior appreciation of what is beautiful." Similar words include "aestheticist," "decorist," and "philocalist."
Since most of these words don't necessarily mean collector, you could use a sentence like this to make the connection:
Indy was an aesthete collector, searching bustling Marrakeshi markets and abandoned Scottish castles in search of the next great find.