Uni degree for IB

One of the doubles majoring in either finance or economics would likely be favourable, not necessarily because it will help you "stand out", but more because those are the main degrees you're competing with. I'd say that Engineering might edge out a little bit for S&T roles, whilst Law may help a bit more for IBD, but the difference is really minor. The maths aptitude required in IBD isn't that significant relative to trading/derivatives, and as such they're not really looking for maths/engo university medallists for those roles - the critical reasoning and logic process taught in law is much more useful, but again this is splitting hairs. 

The main point is, you're going to want that double degree because it will make life so much easier for you - I have a mate who went down the single degree path and he ended up having to extend out his degree in order to have a second crack at internships because he didn't have the requisite experience the first time round, and fair enough, for such a dense and competitive market as it is over here, it can be hard to get a single internship in the 18 months from starting the degree to interviewing for Summer Analyst roles.

The one exception to everything I said above about degrees (and an option you may want to consider if you're currently in High School and keen on IB) is UQ's BAFE (Bachelor of Advanced Finance and Economics) degree, which is specifically tailored towards IB and funds management. It's a 4 year degree which tends to place exceptionally well and is very well respected (more in sydney than melb/perth, but true regardless). Price of admission is a 99 ATAR, but it's still a worthwhile endeavour if you can hack it. 

Having been through a Comm/Law degree, I can tell you that the extra 2 years definitely helped, not only because it gave me more time to get experience, but also because I was able to get a better handle on the content. Unlike in the States, in Australia, they will grill you on technicals regardless of what degree you're doing. Because the cohorts are so small and because interbank week is so compressed (if you didn't know already, you get interview invitations on the monday, and go through three rounds of interviews before offers by close of business friday), the banks simply won't waste their time interviewing people studying an Arts degree, when they could interview someone from a finance or STEM background that is equally capable and doesn't require a basic lesson in financial mathematics when they commence their internship. 

Uni Marks are crucial when breaking in. If you've got an average below 75 at a Go8 or 85 at any T2 uni (UTS, MQ, QUT, etc), you're straight up not getting an interview without a connection, and even if you get an interview through a connection you're going to really have to make your case as to why they should hire you over someone who worked hard enough to get the marks required to push them past the automatic cutoff. As silly as it sounds, at some banks, your ATAR will be requested in your application and serve as another datapoint to which HR can cull applicants easily. It's not a practice everywhere, but I know UBS and some of the boutiques do ask for this (although oddly enough not Goldman or MS from memory). Remember, every summer each bank takes on maybe 3 interns per division at the very most (less in years like last year and this year), meaning that you're looking at potentially up to ten thousand people applying for something like 200-300 roles. 

As for which uni to study at (I know you didn't ask this but given the other commenter mentioned target/non-target I figured I'd touch on it), your best choices are UMelb, USyd, UQ, Monash, UNSW, or UWA (Perth only). If you can't get into those you should either go to UTS/Macquarie and try to shoot the lights out and transfer. Breaking in from the latter two is possible but much more difficult, and transferring in itself isn't too hard so long as you're able to get a 75+ average in your first semester or two. 

As for the point on networking, again whilst it's important, I found it had little impact on my eventual outcome. I had networked hard in the leadup to recruiting season, but the bank that I ended up at (and the banks that I interviewed at) were all those that I had weaker or nonexistent networks at. As it's such a small cohort, breaking in is brutal, and networking might get you an interview, but ultimately they will choose someone that's marginally more qualified than you over you every single time, regardless of how hard you network. There are obviously exceptions to this, but unless you're the child of a superfund CEO or related to an MD, this is broadly applicable.