|You can either buy a wireless access point (AP) or another router that's wireless capable.|
I would go with whichever is less expensive. In either case, you would plug the AP or router into a LAN port on your existing router.
If you go with the router, you might find it's less expensive and you can get one with 4 LAN ports to ensure you have enough of those for wired connections, you'll want to click on my name above in this response and read my “how-to” guide titled, “Add a second Router to your LAN”
It will explain how to correctly add a second router to your existing one. You'll want to use the version where you connect the two routers LAN port to LAN port and keep everything in a single subnet.
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.