Okay, cool. First off, I should clarify - I'm firstly addressing your last question in the last paragraph of your original post; that being basically, "should I even invest?" Good question to be asking.
I think you should invest, and I'm glad your interested in it. Learning about it can initially just be books, but you also asked about actually investing, so I'm addressing that.
Given that you've asked for opinions, here's mine, as if we were sitting together over a cuppa and you wanted me to freely tell you what I think.
I think you are going great, and you are investing in yourself, through your education.
What I'd like to see you do is actually get some of those if's and maybe's solidified on paper, even just an educated guesstimate.
I'd like to see you roughly work out how much money you need for some of those goals.
You earn $1,625 a month which is great. If you're saving half that (after paying your parents and some spending money - I am totally guessing), you'll save another 20k in the next 2 years.
Okay, fine. What I'd like to see you do is budget for that overseas trip (where you're not going to be earning, presumably). I'd also like to see you earmark money that you're going to need in 3 years time...starting a new job, needing a new wardrobe (possibly) and those moving out costs - as well as a car (and I totally agree - your first car needs to be el cheapo). Hardly anyone is that responsible, but it sounds like you might be - I wasn't - but if you ask me my opinion, I'm going to tell you. That amount of money has to come from somewhere and you can earmark funds now for those things. Work out roughly how much, on paper.
Sure, invest it - but that should influence how you invest it. Now, maybe the 20k you save in the next 2 years - which was a total guess - covers all of that. Work it out on paper. If it does (or something like it), your 25k is freed up to invest.
If you are as smart as you seem to be, you should be able to think long term enough to realise that when you are out on your own and working, you should have a rainy day / emergency fund. Some people might roll their eyes and say that's way too conservative for a young person and / or that you could invest it now for later anyway. I disagree, and I only say that because you have the opportunity to set yourself up. Taking my pretend example above, one step further, let's say you decide on a 15k rainy day fund.
So now you know you need to save over the next 2 years (prior to overseas) in cash, and - if I've managed to convince you - another 15k of your 25k as cash (rainy day fund).
Now I'd take the rest (in this pretend example, 10k) and definitely invest that. Like, it's the beginning of your (hopefully early) retirement fund! Once you get your first job, and you've done all these things, you'll have an emergency fund, be debt free (apart from HECS), have money to set yourself up - as well as an investment fund! Like, that's pretty good for a young person just starting out! Then all you'll need to do is make sure you're on a written budget and keep saving for your early retirement plan!
Does that make sense?
So invest, yes. But have a plan over the next couple years to cover everything (the car, moving into a place, your owverseas trip etc)...including a rainy day fund. So don't do anything fancy with those funds (one example would be an online saver, at 3.50%).
If you're with me, and like my crazy plan...then you'd just invest your initial and ongoing capital probably in something like Warren Buffett would recommend - i.e. index funds or somesuch. Nothing wrong with that. The message in a book called, Mind over money (written years ago by an Australian who was in the financial field but also a psychologist) was basically - you dont have to do anything special. You can become wealthy being average.
Learn investing / read books etc. But my opinion (remember, same as if we were chatting over coffee) would be that you dont need to be picking your own stocks etc yet. Most people shouldn't! More important to keep your savings up through life, even as you get married and save up for a house etc. You can do it!
Just a disclaimer: none of this is financial advice - for that you need to see a financial advisor. This is, once again, my opinion and what we might chat about over a coffee. Having said that, I'd be quite happy for ASIC to read my post, as it's some of the most sensible and conservative advice you could get (if it was advice, which it's not, ha!).
One thing I'd steer you away from? Doing anything exotic or weird. You just don't need to. Not even trying to learn to trade FX short-term, or whatever the current fad is. You just don't need to!
If you like learning about investing and genuinely want to pick your own stocks - fine, but that can come later. You might also find yourself more attracted to property investment as far as going deeper on a subject. All well and good - but sticking with the basics is all you need for now.