It's not a case of first in, best-dressed with regards to classes, but again, I can only speak for UNE (it's probably very similar across the board anyway). Once you enrol in a course, you have to do the compulsories. They cannot turn you away because they've already put a certain number of people into a unit.
However - and this is where it may differ between UNE and USyd - we get to choose our tutorials or workshops and practicals (tutorials are like school classes; workshops and practicals are like high school science labs), and then it is a case of first in, best-dressed because you need to structure your timetable accordingly.
The real difficulty you may encounter in the fact that you only have space for a certain number of units per year (at UNE it's eight) and you may have more than eight compulsory subjects to do, so you'll have to do some first-year subjects in your second year if this is the case (I have to do one in my third because we can't enroll if we have a clash and no combination of units let me do one of mine ...).
Generally, there will be people on-hand to assist you. It's easier when you're staying on-campus because you know exactly who to see, but I would be surprised if they don't offer one-on-one course planning in the days leading up to enrolment. However, because first year is usually made up of compulsory subjects, you shouldn't have too much of a problem.
