Regarding "requirement where I need to install Visual Studio on one of my machine and build an application, and manually deploy the application to Azure App service" , any of those editions of Visual Studio will offer that. You can also do that with VS Code
In terms of cost, Community is mostly free:
Just make sure you tick this while installing:
Regarding 2019 or 2022, you probably want the latest. You can still create/maintain same .Net versions as 2019
Case that information helps, don't forget to vote or mark as Answer to help the community. Cheers!