If you will only have 2 speakers in each zone, you only need a stereo receiver. If you will do HT and want surround sound in the room where the receiver is, you will need a HT receiver.
There are a few ways you can do this too, and they were discussed recently
here.
I just did an install similar to this, though it lacks some flexibility, it gets the job done. I used a stereo receiver to an impedance matching volume control switch box to 4 zones. With this setup, only one output from the receiver is used, and power is distributed to each zone which each have volume control and the ability to be switched off (via a/b switch, with b not connected). They are only using 3 zones, and the speakers are smaller and easy to drive, so I didn't feel there was a need to add an external amp. I used an RF remote for the system so they can control the CD changer and overall system volume from anywhere, and it works quite well.
The alternative would be to use a speaker distribution hub (amplified however you like) and send the signal to an impedance matching volume control in each zone, and then to the speakers. This gives you direct control over volume when you are in that particular room.