Best way to enable sorting by 3 criteria on a page of listings

Could you clarify, I think what your asking is if your able to specify post types when querying – you certainly can.

http://codex.wordpress.org/Class_Reference/WP_Query#Type_.26_Status_Parameters

If you asking about category searches, then yes of course. That same link also has information on querying taxonomy, there are many ways to do that thought that depend on the actual site being built.

Edit: From the comments it seems you need to Orderby metadata..
http://codex.wordpress.org/Class_Reference/WP_Query#Order_.26_Orderby_Parameters

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