Query specific posts as determined by end user?

Okay so this may be a little different than most people do. Basically what I’m doing is trying to show certain posts that are determined by 4 different “categories.” I have a large database full of “products” (I’m using the WP Products plugin, but I can not use it if necessary) that when a person comes to the site, they’ll have 4 drop down menus to chose a specific category in each menu, and then query the results determined by those 4 categories.

I’ve been looking into query_posts or $wpdb to implement this. What is the best route to take in this situation?