Hi Tilly
You can't choose the iniversity or TAFE until you have decided what you want to study, my love.
Start here:
Is your occupation in demand? - Workers - Visas & Immigration
Thie above is the Migration Occupations in Demand List and is the list of skills that Australia is most short of at the moment. However, teh MODL does calter according to what skills they reckon they will need to attract in the next 3-5 years or so.
Therefore the trick is to try to guess at a skill which is likely to stay on the MODL and train up for that.
Next, whatever course you do must be one that is approved by CRICOS. So the next step is to work out which colleges or unis offer the CRICOS course that you want to do, and then start narrowing the choice of which collage down from there.
Here is the CRICOS website for you:
Best wishes
Gill