Hey there, small online store owner here, so I deal with a lot of shipping all the time because most of my products are overseas. So yes a good shipping company is important because you would need someone to handle not only the actual shipping part, but the collection, packaging (re-packaging if necessary) and delivery of orders to the customers. I highly recommend using 2 different services in this case:
1. E-commerce platform
Like shopify or Bigcommerce - so what does this do exactly? It organizes you products and transactions, so you can see exactly how many items you have, and how many transactions have occurred. Most of the e-commerce platforms work by taking a percentage from each successful transaction (between 0.5% and 2%)
2. Fulfillment service
A reliable ecommerce fulfillment service is shipping+delivery all in one, you can go about finding one depending on your majority customer location. Mine for example, is based locally (click here
for more info), but if you are located in another country then definitely go local (it will save you a good amount of money)
Hope this helps!