Re: iCloud Library off on Mac, How to transfer music to iCloud-enabled Phone and other issues
Make sure you have logged into the store in iTunes on the new machine with the Apple ID you use with your devices.
Connect up each iDevice in turn but *do not* sync them yet.
Instead cancel any auto sync that it tries to do and then right click on the device in the iTunes sidebar (if you're on the latest iTunes, turn the sidebar back on for this (View > Show Sidebar), or command+option+s.
Then select "transfer purchases" and it will move all of your purchased apps and music from each device onto your iMac.
When it has done that, do the same right click action and select "back up".
Now each device has everything you bought from iTunes on the iMac. You just need to move across any manually ripped music from whatever machine you have it on (your old eMac?). Transfer this by hand over ethernet or via a USB stick or something.
You don't have to pull all your store content back from the cloud, although it is convenient - USB is much more effective if you have a data cap to worry about!
Edit: you also don't have to use iCloud really - if you back up to the cloud it will store your phone settings and contacts, calendars etc, but not your music or apps, since those are already in the cloud. If you back up to the iMac then it can restore everything back just the way it was without having to pull data from the cloud.