There are basically two components that need polishing for .NET Core to be a reasonable choice - the implementation of NetStandard 2.0 for .NET Core (so you get all the old APIs back), and for the tooling to mature (transition from project.json back to fsproj). These efforts are coming along nicely [1][2], but still aren't ready for prime time.
Here's a roadmap that Enrico Sada has laid out to get the F# .NET Core situation to maturity: https://gist.github.com/enricosada/6f0a0424ca65b9d08e5a84f79...
And by the way, don't worry too much about switching over from Mono to .NET Core. With NetStandard 2.0 the API changes should be minimal. Similarly, once the cleaned up proj file format is out of preview the change in tooling from Mono to .NET Core should be minimal (or even non-existent).
[1] https://slack-files.com/T04BJKUMU-F2ST232AJ-6e68200a3d - Enrico Sada's work on getting dotnet cli to work with proj system for .NET Core [2] https://twitter.com/sforkmann/status/790488306991661056?s=09 - Steffen Forkmann getting Paket to work with new proj system
It's even more confusing that there is absolutely no mention of .NET Core on the language's Github page - http://fsharp.github.io/
Also, .net Core does not have feature parity with .net4.6/mono, so you may want to know the gaps depending on the type of application being built.