I've been through this one, it's fairly straightforward as Unis and Colleges love the higher fees that foreign students pay so welcome you with open arms.
For the bricklayers or mechanics course you are more than likely looking at TAFE. I used to work in the international students section there and if you contact them you'll get all the info and help you need. Rather characteristic of Oz, each state has it's own TAFE system and courses but this link for NSW should be a start.
DET International - TAFE NSW International Students - Your unique Australian study experience
The drawback with the student visa is that you are limited to working 20 hours per week max term time, but any hours during the holidays. You will also need to take out compulsory private medical insurance as this is normally a condition of the visa and enrolment.
Hope this helps.