The Arc and Amp do not need to be wired together, as they will communicate over there own  5.o GHz network.  You can connect them via network cable, but it is not necessary.

Personally I would not use ceiling speakers for TV sound, but no doubt there will be other users on here who feel differently.

Hi John, what are your thoughts on the integrated wall speakers SONOS offer. When it comes to speakers what would you recommend.

Thanks for that. Could you link them directly to each other using the ethernet cable (not through LAN switch)

That would be good, but honestly, you don’t need such high quality speakers for surround audio duty.  You could use Sonos One, or cheaper  in wall speakers to save some money.

I believe so, but not 100% sure on this.  John or one of the others should chime in to confirm this. It’s not done very often.

You could do, but the line will be dead if the system is in WiFi mode.  Ethernet ports on Sonos devices are only enabled when the system is in ‘Boost’ mode, i.e. at least one Sonos device is wired to the network.

But even if that condition is met, Sonos HT systems are designed to communicate within the HT setup using their 5GHz radios, as mentioned by @melvimbe earlier.  There is no point in trying to thwart this.  An Ethernet connection is unnecessary, and possibly counter-productive.

To pick up another of your questions, I am not qualified to comment on speaker choice.  But I agree with @melvimbe that for surrounds, One SL speakers would do a very good job, with much lower cost than an Amp and in-wall speakers.  I do understand that aesthetics may come into this decision also.  And where your power sockets are located!

Thank you @melvimbe and @John B 

I have taken your comments in and decided to go for the following

Sonos Arc and 2 x SL One speakers on stands (behind sofa).  This removes the need for cabling and amp, which will save a ton of money.  Then if I find i want to go for a 5.1 system I will just add the subwoofer.  Also with the two SL one speakers on stands there is more flexibility as these can be moved to point out in to the garden space through extension doors.  I also might look into purchasing a SONOS move speaker (with the money I will save) which I can locate in the kitchen area of the new extension.

Sounds a good plan.

For music playing you can set the rear speakers to AMBIENT or FULL.  By setting to FULL you can ensure there is plenty of volume from the rear speakers when pointing at the garden.  You can also adjust the relative volume of Arc and surrounds in the settings.  It’s a bit of a faff to separate the surrounds from the Arc so as to just play through the One SLs, but I don’t think you will need or want to do so in your scenario.