How can I integrate the Shopify checkout process into my app?

[DavidWie]

hello
I would like to integrate Shopify Checkout/Payment with our application to connect orders creation in our application (not yet Shopify app) with Shopify orders. I would like to use Shopify Checkout. Is it possible to do this process by creating only simple  app on Shopify admin and use key and secret from this app or need I create app channel and put all logic inside this app?
Could you give me any advice where to start for creating such app?  The conception of this application:
- this is a standalone app/website but I would like to integrate the checkout process with Shopify using  Shopify Checkout/Payment - I use only few products from Shopify inventory.

Now my application use Shopify Rest API and a simple app (only keys from this app for REST requests) but the Checkout process is independent from Shopify.
Thanks for any suggestions!