Yes, you can use any WiFi router, as 802.11 standards are universal. Netgear and Apple are the best two medium and high end brands, and the best budget brand is TP-Link (their stuff is incredibly cheap).
Wired routers aren't necessary as all WiFi routers contain Ethernet ports. If you need more ports connect a switch. If you absolutely have to have a wired router then you want to set the router up in bridge mode which makes it just an AP.