I have deployed it a couple of times now and each time is a pain in the #ss so I finally allocated some time to put it together in a nice repo so that everything works nice and simple.
Now what this will deploy is a resource group with exactly those resources, nothing more, nothing less.
What costs is the App Service Plan (I chose a B1) and the PostgreSQL server (I chose a B1ms) and it runs smoothly with those but obviously you can choose your own SKUs to suit your own needs. If you take it as is, it costs roughly $28/month