Oh no, I am going destroy you.
Your second option is correct. From the wall comes your modem first, out of the ethernet port on the modem to your WAN port on your router. From there you can connect your first PC to any of the four LAN ports on the back of the router.
The wireless part is pretty straight-forward. Make sure you have wireless security enabled (I suggest WPA2-PSK for the strongest security if it is available. If not, WPA).
And when it comes to TP-Link, I have the 722N USB adapter. It was $20 USD and works great for most applications.