What exactly would you want to do to it? My experience (and I did quite a bit of electronics projects back in the day) is that if you build the housing for a project yourself, no matter how hard you try, it will always look home-built/projectishly. Which kinda defeats the purpose of using it as a showcase.
Unless you have a very big toolshed and/or access to a 3D printer and stuff, you’ll be stuck with wood and/or metal for the case and it is very hard to use those materials privately and get to a satisfying profesional looking result (unless you are building a chair and even then :-)).
Wish you luck though and if you do decide to do it, be sure to post a pic of the result.
Greetinx,
C.
p.s. 1 tip if you are gonna go ahead with this. Try making a transparent case from plexiglas, stick in some nice LED’s. Show the inside of it.