Hi and welcome.
I'm sure everyone would recommend an excellent first step would be to buy a catalogue, so you know exactly what different coin types are out there and how rare and valuable they are.
Here in Oz, there are two: the "Pocket guide to Australian Coins and Banknotes" by Greg Macdonald (known as "Maccas") and the Renniks "Australian Coin & Banknote Values".
But here are some gleanings from what the catalogues tell us.
Scarce Dates: many are hard to find, but aren't necessarily valuable in less-than-uncirculated condition.
5˘: 1972 is key. Some others, such as 1985, weren't issued for circulation and is only found in sets.
10˘: 1972 is also a tricky date, though not quite as tricky as the 5˘. 1985, 1991 and 1997 are some more modern scarcities.
20˘: 1971, anything between 1983 and 1995 can be hard to find (most weren't officially released for circulation).
50˘: 1972 to 1974, 1985 to 1993, and
1995 1997 are the hardest of the "regular" types.
The dollars are complicated by the multitude of mint-your-own and other NCLT issues.
$2: there's nothing particularly scarce; the 2001 seems to be the lowest mintage.
Varieties:Apart from the ones already noted, others that come to mind are:
- The double bar 50˘ of 1966, 1979, 1980. Look for two lines sticking out of the back of the emu's head.
- 2000 Millenium 50˘, incuse flag.
Edit: Thanks for the correction to the 50˘, JAB.

Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis