moving to a new home

Sure.  Just use the same SSID and Password you had at the previous location.

I (generally speaking) wouldn’t. I’d do two things, though. First, at the last possible moment, I’d factory reset everything, and second, leave instructions for the new homeowner where to get signed up and a controller. Oh, and make sure you label the wires, where possible. I used a label device (maybe a p-touch?)

Went through this with a friend, it was harder than I expected, because the previous owner hadn’t factory reset anything, which meant trying to connect with their account initially, but once everything was updated and factory reset, it became super easy. The ultimately hardest part was identifying which Amp (they were, at the time, all CONNECT:AMPs) went to which set of speaker wires, as all the wires had been disconnected, likely to get the Amps out of furniture that was being moved. 

My question is should I take the equipment in the picture 

Thanks — so I don’t need to buy them for stand alone speakers in the new place ?

Depends on what you mean by ‘stand alone speakers’  if you mean third party speakers, you’ll likely need them (although I’d replace those CONNECT:AMPs with Sonos Amps (like the black box one in the picture), mostly for power purposes. If you mean Sonos stand alone speakers, they’re self powered. Depending on which type you get/have, they’re self powered, and  likely have a line in. If needed, you could add a Sonos Port (which looks a lot like a Sonos Amp, too). 

Really all depends on your plans.