How should I approach multiplayer?

Hello.
I am looking for advice for my final year project at University. I have experience in game development for Unity in C# and wanted to make a multiplayer game.
I have never made a multiplayer game, however I had three ideas.

LOCAL MULTIPLAYER OVER TWO SCREENS
Imagine a local multiplayer game where each player would have their own screen. So one machine (PC with two controllers) and two monitor display.
I’m not sure if this is even possible. I remember on the PlayStation One there was a formula one game that used the PlayStation Link Cable. It allowed two PlayStation One systems to be connected and allowed local multiplayer (for certain games) to be on two individual TV screens.
I was wondering if something similar was possible in Unity.

LAN MULTIPLAYER
As mentioned I have never done any form of multiplayer or networking for that matter. I was curious if anyone could offer some advice on a total beginner for networking a game. The requirements of the game are simple and I will list them if it helps…

  • Two Players only
  • Simple controls - move, jump and an action button

The game will be a simple side scrolling platformer. There will be no need for communicating between the players.

WEB PLAYER
I was wondering if it was possible to have a networked game sing the Unity web player. I have never developed a web player game and have no idea how feasible this is.
Or even using two PlayStation Vita systems for local multiplayer.
Any advice is greatly appreciated.

Here’s a tutorial that might help you understand how basic authoritative networking works: