connecting Bluesound node 2i streamer to old system

It looks like I will have to add a good WIFI extender behind my existing stereo system in order to connect the Bluesound streamer.  Most of these better extenders have an ethernet port on them.  Does the Bluesound node need to be hardwired to the extender or does the Bluesound virtually "pick-up" the WIFI and not need to be hardwired...or is there the choice of one way or the other relevant to the best sound.  
"Does the Bluesound node need to be hardwired to the extender or does the Bluesound virtually "pick-up" the WIFI"

No and yes.
What is best? Or, does it depend one way or another depending on specific circumstances? 
The Node has an ethernet connector in back.
I use my Original Node (non 2 or 2i) with a Netgear router to give me 5ghz band wireless.

I'm assuming you have gone on the Bluesound website to follow their instructions to allow your Node to connect to your network. That done, it should "see" it once turned on. The light is initially red, then turns green while searching, and finally blue when connected. If an ethernet cable is plugged in, it will defer to that and connect to your network immediately showing the blue light..

If your network doesn't reach your listening area, then yes, a good extender will bring the Wi-Fi closer to your system and the Node should be again set up via their website to "see" the "new" network created by the extender which will have the same name as your primary one but with "_EXT" following the name meaning that you are now on the extended version of your network. This will require your password (router Key) again.

I actually dealt with this the other way around by moving the router downstairs near my listening room and ran an ethernet cable to my system. Then I installed a NetGear extender upstairs for our computers which run via Wi-Fi.

Hope this was helpful, Fred

no offense meant, I feel the same about my Sonos, tweaks or wifi/ethernet don't have a great effect on it's sound, so I do wifi because it's easier...I believe theoretically a direct connection works best but can add other problems and costs that a Sonos or Node do not warrant...