Hi Andrew,
Did the majority of my training in the Melbourne area so I speak from first hand experience, but this is purely my opinion...
Essendon as you say can get busy at times and doesn't have the training friendly feel that Moorabbin say has.
Depending on where abouts you are located, Point Cook is an option too, however I strongly recommend Moorabbin as it offers a good number of schools who all train toward PPL level.
Moorabbin specific, I would be looking for a place that has a decent number of aircraft, with some experienced instructors and not too many students.
Melbourne Flight Training-
www.melbourneflighttraining.com.au is one of those places which has a great fleet, excellent instructors and a good feel to it and most certainly would be well suited to completing a PPL. If you read Australian Aviation you will find a regular columnist there is also an instructor at MFT
Other options include Royal Victorian Aero Club, Moorabbin Flying Services however if it was me I would personally be going with MFT, great environment and training on offer.
Good luck with the training!