I've done the Australia Post medical test twice in the past. If you can walk, see and hear properly to a certain degree, then you will pass it with flying colours.
Basically, they do the stuff that other people have mentioned here already, so I won't repeat them again. So just be prepared to do a urine test, have your knee hit with a hammer and have yourself weighed. Basically, blood pressure, reflexes and so on will be tested.
You have to fill out the form before you go in (if you didn't already get it), which you'll probably end up ticking NO to most of it since it asks you if you have about 100 diseases, to which you have to tick YES or NO.
As for the police check, well if you haven't committed a major crime, then again you'll be fine. Because your working in a government place that deals with private and confidential information (other people's mail) then they have to background check you, so you're not likely to steal any mail. That's pretty much the first thing they'll tell you at induction, is that stealing mail is a jail-able offense.