I've tried a few fulfillment services, including Shipbob (in the US), I still go with Amazon FBA.
Shopify fulfillment (shopify.com/fulfillment) should be pretty good, but as far as I know it's limited to sellers doing an average of 10 orders a day.
The flow I use:
- Send inventory into Amazon warehouses
- Connect the Amazon FBA fulfillment service to Shopify store
- Fulfill orders on Shopify through Amazon
- Now you have 2 good sales channels - website + Amazon
Here are the details on the setup, including how to automate it: speedboostr.com/automate-order-fulfillment-on-shopify.
Side bonus is that you can launch new products / variations on Amazon to get data on what people want. This is especially helpful when your website / brand is new and you don't have an audience yet, because it's pretty easy to get a lot of views on Amazon.