What's your end goal? Do you want to be able to play multiple sources of music across multiple zones (and not always the same music in each zone)?
Assuming the above, I'd reccommend going with Sonos. A Sonos amp, which can power a couple sets of speakers, will cost you $500. Each Sonos amp is essentially 1 zone. So, for each amp, you can have a different source of music playing. Or, they can all play the same music. And it connects to your iTunes so you won't have to use the airplay. And it's all controlled from your iPhone / iPad / Android.
In the LR, do you have a 5.1 speaker setup? If so, you'll want to get an AVR for the LR and use the Sonos Connect for that zone. Same thing as the amp except it doesn't power your speakers, it just sends the music to them through your amp.
There are other solutions, but this is by far the easiest. You literally plug the speakers in, turn on the power, and press the connect button. 1-2-3 and you're done. And you can work with your budget. If you only have 1k to spend now, start with 2 amps and add on as you want.