It doesn't really matter, you could use whatever you feel for.
In essence it's made with
That's it.
Behind on the serverside there's a database and a server side language.
Whether you use DigitalOcean or another host is also not so relevant here, as they all provide the same functionality. You would probably go for Linux, which almost all hosts offer.
You can get real time synchronizations between users with either JavaScript WebSockets or call the server often to ask for changes, the sockets are probably the better way to avoid overhead.
To get started, I would personally choose
But it's just as saying whether you make sketches on brown or white paper.