Something like counter strike.
AFAIK, network game is hard, and Unity is not good for network game. Is Unreal or Cryengine support network better? What is the best way to make network game?
In game development overall (programming, art, audio, design, whatever) there is not such a thing as ‘the best way’.
You can make an online game with Unity, Unreal, Cryengine and ‘by hand’, just keep in mind you need a server with a decent internet connection for this.
Having a ‘network’ game without a server is like having an Empire State building without the ground floor.
And as for ‘fastest way’, it all depends on what your capabilities are, not the tools you will use.
I’ve seen multiple people creating a Super Mario Bros. clone in vim and g++ faster than in Unity (and vice versa too).