Hi,
This is how I do it:
1. I wrap this script
https://www.phpjabbers.com/food-delivery-script/ (being careful that this is not the only element/item in your app - or it will be rejected on the stores)
2. I then use a linked payment gateway (In South Africa - a local one is PayFast
https://www.payfast.co.za/payment-methods/) to collect the funds. (REST Api)
You could use the script as your main focus, but then add items such as delivery tracking (using native items such as location on Google Maps etc), Push Notifications (Especially NB6 with Big Picture) to promote "Specials", rewards and loyalties and customer early warning systems so that when the delivery is, for example, 500m away from its endpoint you can send a PN with a custom sound to warn the customer that they must wait for the doorbell that will ring imminently !!
That's a bit more than your question of options, but most payment gateways have a REST Api and a relatively easy to integrate - the trick being cost - some of them charge as much as 3.8% of your transaction amount - but this is for your client to decide.
Have a lekka day !!