Another mature aged student here. Sat my STAT test last year in August, both the quantitive component and written English component (as required by all WA unis), applied for entry into first year Psychology with my STAT results, and now here I am, a first year Psych student at almost 38 years of age. I too started out by going to my state's Tertiary Admissions website and finding out firstly when the next STAT test was, and then talking to Student Services in a few unis, just to see what prerequisites I had to meet to get in.

It really wasn't all that confusing once you started to get some info together. So start with the STAT test first and the rest shouldn't be too hard to figure out. Good luck!