Hi intotherealworld :) welcome to the forums,
currently living in Perth, but my brother is also about to start working as a doctor too, so I guess I can relate a bit xD
1) for reducing taxes, your biggest reductions would be taxable deductions, in the form of deductions for expenses like education, books, uniform, laundry, travel and parking. Any of these that have to do with the earning of income at your job, you can deduct. BUT i highly recommend you check the ato website for further detail. If you intend to deduct, MAKE SURE YOU KEEP RECIPTS!! As someone who has worked with the big four and seen a client get audited, I cannot stress the importance of keeping documentation and evidence!
Another possiblity is tax offsets, but I doubt you'd have access to any that could help you there. Yes, contributing extra into super works and that gets taxed at 15%, but if you're anything like me and hate working because perth (or more other corporate environments in Australia) have crappy office politics (yes applies even to doctors), you'd wanna get out fast. But its always an option.
For trusts, you should definitely consult with an expert. I've worked on the tax returns for doctors before and I'd say you would benefit a lot more from a tax expert than without one, especially since your payment for tax services with accountants is deductible too!
2) Personally I recommend starting with one like VAS to VTS (which are exchange traded funds ETFs), for the cost of $20 on average in brokerage, you can buy a parcel of shares each month, which is a great way to start. Great advantage of ETFs is that they have much lower management expenses than index funds, even despite brokerage costs (that is if you are buying >$4000 each time). If you are still 20-30, I would definitely prioritise an emergency fund first and foremost, and then after decide what asset allocation you want. (personally if you feel secure in your job and you have 3-6 months worth of reserves, I would go 90 stocks - 10 bonds, or 20 bonds - 80 stocks).
If you feel a bit undiversified, get both VAS(australia) and VTS(world) and VGS(govt bonds). This is a pretty classic model that a lot of investors use, and would pretty much diversify you well across the asset classes :)
3) Honestly its a big judgement call here, in the long run property will definitely pay-off, the main factor comes down to location and the "quality" of the property. I would highly highly recommend getting an expert to survey any property you want to buy, since the layman wouldn't be able to identify such issues.
In terms of main residency, if you call it main residence for 1 year, and rent it out for 1 year, as long as you establish intention that it is your main residence, selling it later will not accrue capital gains, UNLESS you are out of the property for more than 6 years. But I must warn you that investing in your first property is something you should research first, and one strategy is maybe to rent in the area you intend to stay and scope out the "feel" of the area first.
Edit: Also, i forgot to mention, but you if you have any debt, I would definitely focus on paying that off first, especially since im sure your debt would be practically 6 digits if you had one. Not exactly something you want hanging around if they ever change the HECS debt interest charges in the future.
Hope this helps :)