What are the most important modules for a shop?

I'm building an online store, what would be the best mods for my needs?

Instead of Dolphin, go out to http://www.opensourcecms.com/ and look at the ecommerce platforms.  Many of the platforms will allow customers to register with the site so they can do repeat shopping without entering all their data again.  Unless you are planning on trying to build an Etsy ; http://www.etsy.com/ and in that case I recommend you go to the market and find the developer with the OpenCart integration.  That module will allow each of your members to add a shop using open cart; which you can see in action at opensourcecms.com; the open cart integration does require that admins set up the shop for the member but he/she might be able to rework to have it where when someone joins, the shop is created for them.

I agree.

Dolphin is not a very good option for a store. The built in store module is for digital downloadable products only. To sell merchandise that is to be shipped the built in store is of no use.

Shop module for physical products is now available at https://www.boonex.com/m/shop-sell-physical-products