According to a blog post on Chad Liddell's blog "The toy vault has 203 total unlocks in it. I’m not %100 certain if that includes unlocks from lucky toys. Hopefully someone in the community will know that."
The post can be seen here:
http://chadliddell.tumblr.com/post/60400334340/spinninSo, if my math is right that would require 9 characters total including the 3 from the starter pack. I've seen many people here say 180 so maybe there is some merit to his comment about lucky toys. I currently have 8 characters and while will most likely get more, it would be nice to be able to unlock everything now to really let my creations take flight.