Question : Switch or 2nd router or Repeater?

There is a Wireless Linksys router in the basement. All the ports on the router are plugged into a patch panel. All the rooms in the house are hard wired.

Of course you still want to utilize the Wireless capabilities of the router in the backyard, 3rd floor etc. But, as you can imagine the wireless signal from the basement is not strong.

I am looking for the best option with maximum WiFi strength.

Option 1:
Add a Switch. So, purchase a switch and plug the cable modem into it, along with all the other  connections that lead to the rest of the hard wired rooms. Place the Linksys WiFi router in the main floor (2nd flooor), and hard wire it. Then configure WiFi that way.

Option 2:
Leave setup as is and add an additional WiFi router to the (2nd flooor), and hard wire it. Then configure

Option 3:
Buy a Repeater

Answer : Switch or 2nd router or Repeater?

All of your options would work, but option 2 or 3 would be best depending on price.  Some routers will act as repeaters and can come out cheaper than buying a repeater.  Option 3 would be the best if cost allows and the easiest to configure.