I have a BT home hub (& Infinity).

Do I need an Airport Express hard wired into the home hub as a base station or just one in each room where I would like music playing? Will these also act like Wifi extenders?

They can be used to extend and be part of an existing WiFi network, so you just need them where you want them – this is exactly how I use mine. Nice and tidy little devices.

An AE can join the BT wireless network but 99% of the time an AE will not extend the network (I.e boost the range) unless an AirPort Extreme is the base station.
So you can wirelessly do AirPlay with your hub but if you want to extend the range you’ll need to buy an AirPort Extreme and hard wire it to the bt hub (switching off the bt wirless and using the apple extreme instead)

Can I set it up with a single AE first then if I change my mind, add an Extreme later?

No reason why not. I have an Extreme and two Expresses.

Absolutely, it’s what I did. An extreme adds extra stuff too such as network drives and printers

Yep, my extreme is a NAS server for several USB hard drives.

If its for streaming I’d look at sonos or squeezebox etc.

My AE can be problematic at times. Either stuttering mid tune or failing to play all together. Only solution seems to be either a reboot or an airplay disable/enable. Neither a quick option. I wouldn’t buy another.

So 3 positives and one negative. Thanks for the info folks. As usual, very informative 🙂