Nowadays, a Microsoft account is a prerequisite for playing Minecraft, so be prepared to either use your existing account or create a new one that will handle all your Minecraft account info and any additional microtransaction purchases you make.
Both versions of Minecraft are compatible with the Windows operating system, despite one specifically being named Minecraft for Windows. Unlike in the past, you cannot screw things up by purchasing the wrong one. Although there are two versions of Minecraft, they're now sold as a package deal and are more equivalent to one another than ever.
