How can I add products to cart and checkout on my own site using Shopify's API?

New to this so bear with me. Looking to build our own website that hooks into our shopify store to pull products and to add to cart, and checkout.

So far I’ve created a store, added some products, added a custom app which I can get products from through REST API.

So, can we add to cart through this API as well? Having trouble finding how to do that. Or do we need to use Storefront API or something else.

Any info on how to achieve adding to cart and checkout on our own site, hooking into our Shopify store would be apprecatied, thx!