@Scott
I read an article in the paper that inspired me to research ATC in January. I applied early February.
I did ST1 mid Feb. I only left myself 3 days to prepare for ST1 as I didn't realise I had to learn the document. For the other tests I just reviewed the material they sent as nothing else is directly relevant. Because they are aptitude tests practice doesn't necessarily improve your ability to pass unless you happen upon almost identical questions.
I did my ST2 in April and did no preparation for it as there is really nothing you can do.
I did my ST3 on Monday July 5th as I had my final exams for my degree in May/June (2:1 BEng Civil Engineering - thankfully now my insurance policy)! Preparation for ST3 involved reading Air Traffic Control by Graham Duke and visiting my local (non-NATS) control tower. I also did some research into competency based interviewing but this didn't really help as you don't know what you will be asked and you need to think of specific examples on the spot in the interview. Basically you will be ok if you can think quickly but will come unstuck if your mind goes blank or if you hesitate for too long.