Christine here from the Shopify Guru team - thanks for reaching out!
To offer product based shipping rates you can use an app from the Shopify app store called Better Shipping Shipping. Better Shipping allows you to create individual shipping rules based on the products and or the shipping address.
Hope that helps! Let me know if you need anything else. I am just a click away :)
A more nuanced answer is that any shop can control shipping with their own shipping responses, whatever they may be, using scripting commands that act according to the checkout details, which Shopify will conveniently send to you.
There are so many shipping exceptions that can challenge a merchant, knowing you can script your way to a satisfactory response is also very important information.
Limiting yourself to recommending one App is like telling someone they can rent a Ford Fiesta for their dream holiday travels. Sure, it's a car, and they do need to rent a car, but really, you want the family in one of those cars with luggage, day in, day out?
You can very easily mark those products which do not go with USPS with a product type such as 'no-USPS' and then frame automation rules in the Multi Carrier Shipping Label app that will allow you to show UPS for these products only. Similarly you can set conditions on other products as well.