That's a good question. It depends on your drop shipping arrangement.

The simplest way is to list the products on your site as if you sell them. You don't need to use Seller or Warehouse features at all. When a customer buys, you simply send the information to the dropship company to fulfill for you. You can automate this step depending on how your dropshipping companies want to receive them. Some dropshippers just require an email so you can automate by setting it up in the Storefront to automatically send an email to your dropshipper. Some dropshippers have an API that you can program (or engage us) to write a scheduled job to send for fulfillment. Some dropshippers expect you to login to their site and fulfill it manually. In any case, the customer is unaware as long as it's shipped out in a timely manner.

The Marketplace feature is intended for vendors (aka "sellers") to list/manage their own products for sale on your site. The sellers are able to login and view their orders and fulfill them without your interaction. It's more you operate as Amazon and these vendors come list their products to sell at your site.

The Warehouse feature is intended for tracking inventory at different locations. This isn't really needed for drop shipping. Warehouse is useufl if you have products in different locations (west coast and east coast) and you need to make sure you only sell your available inventories or you want to make sure customers buy only from the nearest warehouse.

I hope this helps.

How would you recommend we automate the email(s) that would be sent to the drop-shipping company. I was thinking that we could use distributer to determine who to send the email to and provide the email address, but I don't see any distributer information in the input xml to the Custom Action.

How would you sugest we set this up since we will be sending orders to two different dropshippers and both could have items in a single order? 

If you look at your product (Catalog > Products). There's an Action tab, you can select Custom rule. In the XSLT, there's an example template to send email. You can try to send yourself an email by going through your own Checkout. It should send out per product, which means you can set up different emails for different products.