Karlie here from the Shopify Guru Team! With Shopify, you would have the ability to set manual shipping rates by the total order price or by total order weight. Check out this guide to see how you can set up those manual rates from your Shopify admin!
So, if you're looking to set up shipping rates for specific products, you would want to use an app to do so. I've gone ahead and found a few apps that could suit this type of functionality, be sure to check out: Better Shipping, Parcelify or Advanced Shipping Rules!
I hope this helps, but if you have any further questions - be sure to reach out to Shopify support!
I know it is a bit old but, I just wanted to add the Multi Carrier Shipping Label app to the list that will help you handle the shipping cost based on zones, quantity, total weight, price, weight range, etc.