Cleaning an Antique Baby Buggy?

I have an old baby buggy that was used back in the 1800s. It's been in storage, so it needs a lot of clean up done to it. Someone suggested using a furniture oil on the leather parts because it smells musty. I plan on using it as a prop for a baby shower this Saturday. The metal parts are also rusty.

Everyone who has seen it says I shouldn't get rid of it as it's unique. I am 58 yrs. old. I was in it when I was a baby as well as my dad and my grandmother. How should I clean this thing? Thank you.

By Bonnie from Zion, IL