Look into the ETFs VAS and VGS. VAS gives you exposure to the ASX300 and VGS about 1500 companies from developed markets (about 63% US). It gives you instant diversification, super low fee, decent dividend (more so VAS than VGSbecause Aussie shares pay more dividends) and a super simple accounting come tax time : you receive one statement for each, and that's it. Both also have dividend reinvestment plans so you can let the dividends compound over the long term. VGS also has an equivalent with currency exposure hedged called VGAD.
But the most important is for you to look into the concept of index investing as opposed to direct shares picking. It has been proven over the long term the index beats the vast majority of managers, meaning if you select some shares yourself, you are unlikely to do better than the index, over the long term. The other great thing about index investing is the fact that if a company rises - say because they have discovered a new vaccine/mine/technology - it automatically gets added to your holdings, since the ETF reflects the market index. And it also works the other way around: when a company fails, your holdings of it diminue until you don't have any because it's not in the index anymore.
Both these ETFs are with Vanguard, certainly one of (if not the one) big player in this sphere.
Vanguard's website has some good materials on it around education and I suggest you look into buffet's videos and listen to Bogle: he's the dude behind vanguard and one of the guys who has shown what index investing can do.
If you go down that way, you need to remember that for this to work, you have to let time work for you: that is not sell when the market tanks, else you are simply crystallising your losses. The good about this is that you still get paid dividends and if you reinvest them it helps grow your assets and compounding works it's magic. So even when the market tanks, you are still being paid for holding the asset.
Lastly, the large and old LICs (AFI, ARG, MLT) are great - however be aware and careful: these usually trade at a premium to their NTA (basically intrisic value of their holdings). For instance when I last checked ARG, it was trading at an 11% premium, which means you are paying 11% more than what the underlying shares are valued at. The great thing about LICs though is that sometimes - rarely but sometimes - they can trade at a discount which is then a fantastic buy. What a lot of investors do is check the premium and if too high, simply buy the index (VAS).
Good luck!