There's an app called TimeMachineEditor that schedules TM backups for you. I use it on all my macs to do daily backups.
I believe you can set the mountain lion server on the iMac to wake on network access, but there are so many variations... with your setup I dunno for sure.
Thanks for pointing out the existence of TimeMachineEditor! Hourly backups are a bit too much for me, so I'll look into what that utility can do.
And you can configure OS X to "wake for network access," roughly equivalent to Wake on LAN. That's a standard OS X setting (Energy Saver preference pane, maybe?). I think the machine has to be sleeping rather than off, and it doesn't always work for me, but you can test it to see if it does for you if you feel compelled to make your server sleep.
That will work. Actually Lion Server probably does the same thing but I'm not certain of that, I have ML.
You're correct--Lion Server also has a Time Machine Server function. I'd be surprised if it's not present going back to even 10.5 Server where Time Machine itself was introduced on the client side, but I don't know. Of course, Mountain Lion server is cheaper if you don't already have Lion Server. There's no reason to worry about version compatibility--Lion Server works fine for Mountain Lion clients on Time Machine. That's my current setup at home since I'm not planning on "upgrading" my server to Mountain Lion any time soon.