Connect the router to the modem, then each PC to the router either wired or wireless. The wired PC will have faster throughput because wired is faster than wireless. Each PC will share the pipe. If you want full use of the pipe with each PC you'll need two pipes.
We have two computers and two internet connections, one cable and one DSL. We're contemplating going to just the cable internet for both computers. Is there a way to hook up the router to the primary gaming computer without interfering with any of the online computer games? In the past, there have been problems when those with wireless connections try to connect to a game.

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