Well, in most cases the transmission is initiated by the pilot. So if you're asking for a clearance, level change or whatever, that's probably what you're going to get and need to read back. Fairly easy to anticipate.
I only tend to write the things down which I can't input immediately. QNH, squawks etc are put into their rightful place (altimeter, transponder) immediately, sometimes even while transmitting the readback. Level changes, if it is what I've got in my plan and asked for, I don't write down. Anything out of the ordinary, I do write down. And I do write down the ATIS.
Get a (second-hand) scanner. Listen to aeronautical frequencies. Listen to pilots asking for clearance or whatever, listen to ATC give them something, and then try to read the clearance back for yourself (out loud) before the pilot does. Bonus points for spotting the errors of the pilots!