..if you intend on using a desktop in second room, use a simple wired "switch". A wired connection is generally faster than the wireless type.

See an example of a "Range Extender in the link below. It has a 4 port "wired" connection plus it has the ability to use the wireless connection as well. Instructions on syncing the wireless signal with the original router should be included.:


Or, as in your suggestion, the simple Wireless Access Point below would work as well.


Either way, the primary "wired" router setup doesn't need anything connected to it once you've set it up.. But the primary router WILL need to be secured with its firewall and a good password security so it can't be accessed easily by outside intrusions.

Hope this helps.