Any recent version of C# should be able to successfully compile Monogame 3.5 or 3.6. This means that either VS 2015 or VS 2017 should work fine (Community Editions if you do not have an MSDN Professional Subscription).
When you download the source code you should be able to open the Project Properties windows, which will tell you what .NET Framework the solution is compiled for. My own suspicion since I have not looked at the source code is that it would be compiled against version 4.6 of the .NET Framework.
The versions of C# you are asking about are determined by the framework in use. Thus, if you install VS 2017 but compile to the 4.5 version of the .NET Framework, that is the C# version that will be generated for you in terms of your executable and assemblies..
The latest framework is 4.7, which has just been released and is installed with VS 2017 (I believe...). If you compile to this version of the framework than you will be using the latest version of C#.
If you would like to query the Monogame developers about this in real-time, simply go to the following link...
Scroll down to the bottom of the page and select "Chat Live" under the "Helpful Links" section...