I'd suggest wiring a gaming desktop and a PS3. Most gamers prefer Wired over Wireless. If they find out what Steam is, expect the Wireless to get destroyed whenver a game is being downloaded/updated. I'm a PC gamer myself, so this isn't coming out of thin air. :)
Otherwise, use the existing Wired connection nearby to connect up that router in an "Access Point/Switch" setup if you have FiOS TV as well. Otherwise, yes you can replace the ActionTec router (you will need an CAT5e connection from the ONT) with your own. See this guide for more info: https://secure.dslreports.com/faq/16077
Be sure when you set up your router, that the 2.4Ghz band is using a channel the ActionTec is not using. The ActionTec will show you in the Wireless Status pages what it is using. You'll want to pick from Channels 1, 6, or 11 ideally. Overlapping can be used, but in more extreme circumstances. I would also avoid using 20/40Mhz "Auto" mode aka "Up to 300Mbps/450Mbps" on 2.4Ghz as due to noise, this can actually HURT your Wi-Fi more than improve the speed. For 5Ghz, leave it to defaults.