Good Question!
I've created quite a few online stores in the past 6 years and it depends greatly on the volume that you plan to manage.

I'll explain:
If you are running a basic ecommerce site for selling products and your sales process is fairly straightforward (checkout, ship, done) then you will probably do fine with whatever tools are included with your shopping cart software. (Shopify, Magento, Woocommerce, etc).

Now, if you handle a more complex sales process (partial payments, support fees, manufacturing, drop shipping, etc) then I would definitely recommend trying out an ERP or at the very least a CRM to keep tabs on your clients and your communication with them.

There are some nice free tools out there like Podio that can help you create your own custom CRM or ERP to fit your needs (no coding required) in a drag and drop manner.

If you prefer a more hands-off approach, there are tools like Infusionsoft that have automation workflows. You could set up things like: creating a task for a sales rep to follow up with someone has not paid a late invoice in two days. Or send customers an automatic e-mail as a follow up a few days after the purchase, etc.

I hope this answers your question, let me know if need anything else!