Matt, Where are you storing the data currently that would be used to update the shopify store? The reason I ask is updating the shopify store is only one piece of the puzzle. The perfect solution would quickly querry your master data store (database holding the master list with current inventory) for the items that have had a change in quantity since the last update ("yesterday"). Next simply updating quantity on hand in shopify via the API for each of those items, and adding any new items that have been created. Shopify will disable the items that have a quantity of 0.
Our inventory management application - apps.shopify.com/ducotrax-inventory-management - is integrated with shopify, so we are very familiar with the API. Let me know if you would like to discuss some ideas for a solution for you.