Creating A Project
Without MonoGame Installed
If you don't have MonoGame installed you could use the nuget package, use THIS document to do this. It will get you to install the MonoGame package and will also create a project. PS This is not the easy way
With MonoGame Installed
No Templates Installed
If you have installed MonoGame onto your own machine and you don't have the templates, or you are using MonoGame in college for the first time then you should use THIS document to create a new project. You will need to download the template zip files from moodle as described in the document.
By the way, this has happened because when MonoGame was installed you hadn't previously opened or run Visual Studio. Re-installing MonoGame should give you the options to add the templates depending on your version of Visual Studio.
With Templates Installed
If your game is okay for just Windows, I would recommend to create just a Windows Project because it will keep everything simple. You could use another option, this will depend on the platform you wish to target but the cross platform option is a good compromise.