Since you want to ship with UPS and USPS based on size & weight, you can use Shopify shipping. This guide here provides a really good understanding regarding the Shopify shipping process: https://help.shopify.com/en/manual/shipping/shopify-shipping.
Shipping can be set up under the "Shipping & Delivery" settings under the Shopify dashboard. You can create shipping zones based on the countries to which you are shipping, and set up shipping rates for these zones. The rates can be set up as a flat fee or carrier-calculated rates based on your requirement. Since you have mentioned regarding shipping with USPS and UPS, you can use discounted shipping rates with USPS and UPS by Shopify. Check out these guides for better understanding.
You can also check out this video here to understand the complete process: Shopify Shipping.
Please feel free to reach for any issues or clarifications. I'm happy to help!