The kind of development we do probably wouldn't count as "serious" here on HN, but since the other comment didn't really answer your question, I'll pitch in. We've been developing using .NET Core/Linux/Rider for the past two years. It's been pretty great. Once you get to know the IDE really well, I'd say Rider beats VS in terms of functionality and usability.
.NET Core was developed with CLI usage in mind and common operations (like migrations/boilerplate generation) can be driven from CLI or Rider, you don't need VS for that.
You may have some problems with 3rd-party libraries. Not all of them have been ported to .NET Standard. I'd recommend checking your project's dependencies in advance. (We did have some problems with legacy COM-based cryptographic libraries and had to build a separate "microservice" hosted under Windows to offload this stuff to. COM stuff works fine under .NET Core, but only under Windows (obviously).)
If you are just running a few static Windows servers the slight cost benefit of running Linux for .Net Core is really not that great. If you are doing anything more dynamic where you are rapidly bringing “servers” up and down is where you see the real cost and performance benefits. Of course you can’t run Windows instances with either Fargate or lambda but even with regular ECS (Docker) or autoscaling EC2 instances where you can, Windows costs more, takes more resources, and is slower to launch.
.NET Core was developed with CLI usage in mind and common operations (like migrations/boilerplate generation) can be driven from CLI or Rider, you don't need VS for that.
You may have some problems with 3rd-party libraries. Not all of them have been ported to .NET Standard. I'd recommend checking your project's dependencies in advance. (We did have some problems with legacy COM-based cryptographic libraries and had to build a separate "microservice" hosted under Windows to offload this stuff to. COM stuff works fine under .NET Core, but only under Windows (obviously).)