Connecting to the internet on a Mac without airport

If you have a wifi router on the ground floor the then ideal device would be a 'network bridge', also called a 'wireless access point'. This connects to the wifi signal and outputs it through ethernet (which will work with any computer with an ethernet socket: no driver is required). Unfortunately these now seem very difficult to get - a search on Amazon didn't throw anything up but you could do some general searching - don't accept one with a USB connection, that's not likely to work. Obviously the wifi connection has to be strong enough to work three floors up, which is pushing it a bit.

Another alternative is a couple of powerline adaptors - there are several makes available. These plug into the mains sockets and have ethernet connections, so that they then transfer the data over your house's electricity wiring. How well they work depends on the quality of your wiring and the amount of general muck on the mains (there is often quite a lot of that).

I don't know what the cost would be: you could try getting an estimate from a networking company to lay an ethernet cable up to the third floor and see whether that was a viable idea.

The AirPort Express in ProxySTA mode should let you connect the computer to the Wi-Fi network.

https://support.apple.com/HT204371