Hi @curtis,
Thanks for sharing to the Community.
The first step will be to create and customize a Welcome Flow.
If you want to restrict the flow to only subscribers from that pop up, you can use a flow filter to do so. You'd set that up like this example:
For the coupon, you have two options: a static coupon that is the same for all customers, or a unique coupon that is different for every customer.
If you want to use a static coupon, you can just create that code in Shopify and put it in the email directly.
If you want to use custom coupons for all recipients, you can follow this guide to get that set up: Unique Coupon Codes for Shopify
I would recommend checking out our Community articles regarding this:
Hope that helped,
Alex