MVC5 was never released though, and the changes have been rather minimal from ASP.NET Core v1 to v2 with straightforward migration guides, so it might look messier than it actually is if you were working through all the previews and release candidates instead.
Nevertheless, Microsoft has a long history of having messy v1.0 with most of the stability coming after v2.0, so you can consider the foundation pretty stable now that it's on v2.1 and more.
There are some challenges coming up with design changes to the compiler and C# that might overlap what F# already has but it'll get sorted out.
Great resources for getting started with F# at https://fsharp.org/
My personal preference is generally to install the SDK and use the http://ionide.io/ with VScode as it seems to work most reliably cross platform.
I have .NET Core but the whole thing seems to require Mono and it isn't clear from fsharp.org that you can do without.