Do not buy an N range extender -- it will not be adequate for good gaming.
You have a couple of choices that will work. Run an Ethernet cable to the main router -- best results. If not the next choice is to buy a cheap wireless N router and use it as an access point near your computer. It will need to connect to the main router with an Ethernet cable (or if you absolutely cannot do that you can use a pair of good powerline adapters like the Zyxel PLA5205kit instead of a cable). The other more expensive option if your budget can handle it is a pair of ASUS AC routers, one as your main router and one as a media bridge like
THIS.