what is your budget? a 3 zone capable receiver ( denon 4400/4500, pioneer 703) will run you ~700 - 1500 (depending on new or refurb) there are many other systems/solutions.
you could get by with as little as ~100 - 150 / zone (dayton audio from parts express) or Sonos amps ( 600/zone)
overall, I suggest you consider a music of wifi soltion ( Sonos, HEOS, musicast, playfi, etc) on top of some cost effective amplification.
that is if music is your only application.
example: https://www.parts-express.com/dayto...lifier-wfa400-4-zone-wi-fi-audio-re--300-5700
alternative: 3 x ( https://www.parts-express.com/dayto...lifier-with-ir-remote-and-app-contr--300-3821) you will be suprised at what a 20 wpc class d amp can do!. (