Exhibits in the Museum is always a great place to place stuff that you don't want in your inventory. Another way would be to create other characters and use them as inventory space. Other than that I just sell everything else I know I won't need and can buy from the catalogue.
I generally put all of it into whatever PWP I'm working on. If I have any left-over, it goes into my home loan until I have 30,000 Bells. I try not to go under incase of emergencies!