Check out the train map here: http://ptv.vic.gov.au/getting-around/maps/
In terms of convenience, you want to look for:
Places near "Premium" stations, as shown on the map. Not all stations have employees on site, but Premium stations do, so you can ask an actual human if you need help. More importantly, express trains always stop at Premium stations. Express trains are a godsend during peak hours—they're faster and are often less crowded.
Places near stations that are on multiple train lines. This is especially helpful at weekends as the waiting time between trains is longer. E.g. up to nine train lines pass through Richmond, so you can choose to ride whichever train is coming sooner.
If you foresee that you will work in the CBD, places in Zone 1 are more convenient. Another advantage of living near the CBD: trams, which run more frequently than buses. On the Public Transport website, click on Journey Planner to calculate travel times.
If you have school-age children, note that many schools limit enrolment to residents of their catchment or area of jurisdiction. You can check reviews for schools in your shortlisted suburbs here: http://www.myschool.edu.au/
As for safety, it's best if you visit your shortlisted suburbs at night, to see how safe you will personally feel. It can get very dark, with limited street lighting. I have lived in various southeastern suburbs and have always felt safe. I commented on a few suburbs in the VIC thread, I'm linking to that post here: http://pinoyau.info/discussion/comment/81686/#Comment_81686
Good luck and happy house-hunting!