Hey there, @Kuventfy
Bo here from Shopify Support!
That is a really good question. Currently, there is no way to manually order the shipping rates in checkout - they will always default to show the least expensive first; free shipping in this case. I will most definitely bring this as feedback to our developers to consider.
All the Best,
We have this same exact issue and NEED it resolved. We give customers the options to give us their account number for shipping for shipping collect. When a customer gives us the number where prompted they then click the free shipping collect option, no problem, works great. If a customer doesn't give us a shipping account number we NEED the shipping to default to the paid options we provide. This is an embarrassing problem to keep explaining to people who don't read our instructions well enough and thin they are getting free shipping. We end up cancelling orders over and over again and loosing customers who think our checkout process isn't clear/doesn't work which means that Shopify's checkout process ins't clear/doesn't work.
We NEED to have the shipping default to the paid options no the free option. When will this be available