So we can take the easy ones first. Your zone 2 and independent make complete sense. The only decision is between an Arc or Beam. If you are looking at a certain $! Amount for each you could have some flexibility of adding some ones in the back of zone 2 as that would give you a more complete sound around that $700 price or if you want a more expansive experience you would consider the Arc. For example. Your bedroom is similar to mine and I have a Beam and two ones. 
So for your zones 1 and 3, are you just considering amps because you have existing floor or ceiling speakers? If that’s the case then yes that would be about it. If you are not or are building in new speakers you could use some ones, fives or moves and have some more flexibility without the need for wiring to those rooms using an amp. The only way you would use only one amp is if you used sonos architectural speakers with e understanding that both zones would be playing the same music at the same volume unless you added in volume adjusters for each room.  I guess a little clarification would be helpful. 

Thanks. To clarify this is new construction, we only want hardwiredceiling speaks and sound bars, no ones fives moves roams etc. 

Looks like a nice setup.

Your plans are accurate. I would suggest adding a couple of more outdoor speakers to cover the open patio area. You can connect up to four speakers to a single Amp (up to six speakers if they are Sonos Architectural by Sonance speakers).

If you are interested in adding in-ceiling rear surround speakers in Zone 2 or your master bedroom, you would need to add another Amp to each of those zones.

I would also recommend more speakers in the patio area -- with Volume controls for each pair.

Thanks everyone