How to connect home network?

My cable connection comes into the house and a coax spliter sends one signal
to my computer room
and the other signal to my media room. The two rooms are 50' apart and I
can easily install a cat 6 cable
between them, if necessary.
In the media room I am getting more and more stuff that needs to be
connected to the internet,
such as Wii, blue ray player, receiver, etc. In the computer room. I only
have the computer tower.
What is the best way to get this all up and running? I suspect I need to
buy a router, right?
If so, in which room should I put it? This is all Greek to me.
Any advice would be appreciated.
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