next-jdbc VS Gradle

I can't help you with the database part but I think you have enough grist for your mill, so I would use whatever db you know and then connect to it via next-jdbc

3: Postges is fine, i'd recommend next.jdbc to connect to postgres.

Because executing CodeNarc from the command-line is not so simple, I find it easier to use Gradle and its dedicated plugin to execute CodeNarc:

A ("shared") build service is kind of like a singleton, in that when you register one in any project, it's available in all projects as a single instance. (This unfortunately turns out not to be true, in some cases, when using composite builds, but can be worked around.) An actual singleton (global static instance) doesn't work at all, for the record—try it if you want to lose some sanity. Anyway, use a build service whenever you need global mutable state in your build.

When using build tools like Maven or Gradle, you can configure environment variables in the build scripts or configuration files.

For large projects, purpose-made build tools such as Gradle and Maven are preferred for managing the directory structure since they introduce additional semantics for managing test code and other programming languages (among lots of other things). Most IDEs can integrate with these build tools easily. If you're just starting out though, I wouldn't worry too much about these, you can visit them later.

Project Build and Management: Apache Maven 3 (3.9.5), Gradle 8 (8.3)

No wonder this had been raised previously, https://github.com/gradle/gradle/issues/15383

Ktor, a powerful web framework built with Kotlin, offers a lightweight and flexible solution for building web applications. In this article, we will guide you through the process of creating a Ktor project manually using Gradle and SDKMAN!. By following the steps below, you'll have a basic Ktor project up and running in no time.

The details regarding the code compiling would vary from one project to another. For that project, it seems that it uses Gradle (a helper tool) for compiling. Check Gradle's documentation for more information.