Checkout Form radio-button calculation

Hi, i am building an e-commerce website with laravel 5.2

I can add my products to my shopping cart, which is stored in a session. I can view my shopping cart & when i click confirm i go to a checkout page.

All my items on the checkout page are still only in the session. Is this good practice or should i store stuff in de database after i go to the checkout page? .

On my checkout page i have a couple of radio-buttons to select the shipping method. I would like to make a calculation based upon my selection. What is the best way to handle this? I would like to avoid putting a submit button below the radio-buttons to confirm the selection. An important notice is that i also have a field for a Coupon code on this page which i calculate using a get request. So refreshing the page is not really an option because my coupon calculation will be gone.