There are receivers with built in wi-fi operations that can get music from your phone. This is similar to Sonos. While Bluetooth is excellent for near-device usage, it's useless for whole house capabilities. For that, you want to use something which can utilize wi-fi. This can be Airplay (Apple), Sonos (all brands), Chromecast (Android), or Denon has some products with it built in. Sonos is extremely robust with it's capabilities in adding this functionality, but it carries the price tag to go with it.
if that room is already setup, and your $1,200 needs to be for the speakers AND the receiver, then I might just focus on getting a decent 2.1 setup to start things off with and some cheap outdoor speakers.
So, a receiver like this will give you the capabilities for handling all your theater needs and some outdoor speakers with wi-fi connectivity through Heos...
https://usa.denon.com/us/product/hometheater/receivers/avrx1400h
That leaves you about $700 for a decent 2.1 system which can then be upgraded to 5.1 over the years, or even 7.1 then run a separate amplifier for your outdoor speakers if you want to.
For outdoor speakers, just getting some basic audio out there can start at about $35...
https://www.amazon.com/Dual-Electronics-LU43PB-Performance-Bookshelf/dp/B000A5S926/ref=sr_1_4?s=electronics&ie=UTF8&qid=1502823197&sr=1-4&keywords=outdoor+speakers&th=1
But, the sky is the limit on all of these things. It's a decent looking theater, and the projector that's in place is a very well respected entry level model. If you are set on getting 5.1 to start with, then you will be compromising the sound a bit, but there are tons of options out there. Still, a good subwoofer is critical and that tends to be a serious chunk of the budget.