There is no simple answer as every eCommerce business has truly unique needs and as those requirements are outlined it will present a clear case for which direction to proceed. Based on what you've outlined already my recommendation would be to use a platform that has unlimited flexibility to integrate into - most likely that would be WooCommerce but others could work too. The key is having your shipping and fulfillment automated, all of your inventory centrally managed from one place regardless of the channels you sell through (i.e. Amazon + your own site), and all customer communication automated. If those things aren't automated you'll lose your pants on trying to manage the business just to keep up with the daily changes in data. We actually just helped launch a business in a very similar situation https://moringavinga.com/

The last reason I'd recommend doing a combined approach of channel sales through something like Amazon plus your own site is you're not putting all your eggs in one basket that is highly dependent on another business. i.e. what happens when Amazon says to sell that food product your labeling has to change -until then they remove your product and you lose 100% revenue + momentum until you can meet their new requirements. Having a home base for your own brand is critical.