If you're on a tight budget, you could do a simple combination of Wordpress (WooCommerce/Stripe) and MailChimp to gather and store customer information and preferences, process customer communications and shipping notifications, and automate deliveries. It'd be a bit manual for setup, but I'm convinced you could move the data between the systems at low-cost and enable accurate drop shipping, depending on your products. Of course, you'd rely on customer input to store preferences (allergies, tastes, etc.), and this input could be gathered a number of ways, perhaps through surveys or through a customer preferences profile required during the buying process. Once the customer lists are organized and the systems are connected, you could automate the vast majority of it (at low cost). A little bit of hustle to put together, but way cheaper than the fees associated with many CRM systems.