.NET is a good technology if you don't mind being somewhat tied to the Mircrosoft stack: it's well designed, reasonably performant, strongly supported and relatively stable. It has good integration with other Microsoft products, good tooling with Visual Studio and an extensive set of libraries. (The libraries are what would probably tie you the most strongly to Microsoft.)

Functional programming is a much deeper topic, so I'll give my condensed and unabashedly biased summary: functional languages tend to be more expressive (and, transitively, more productive) while producing code that's easier to support--F# has a good type system, and functional programming leads to much lower coupling than OO much less procedural programming. This happens without sacrificing performance too much. Sure, you won't get C speed (or even C# speed), but it's more than good enough for most tasks. I'm pretty sure F# is at most a couple of times slower than C#--much faster than the popular dynamically typed languages! I'm really only familiar with OCaml and Haskell, both similar languages, and they can certainly produce fast code.

So if you're convinced by functional programming and somehow tied to .NET, F# is the perfect choice. If you're not tied to .NET, I would recommend Haskell or maybe OCaml instead.