Firstly, well done on reaching this milestone!
I suggest reading this series (from the first post) by Jim Collins: jlcollinsnh.com/category/stock-investing-series/
(Obviously the stuff about 401k plans and the individual investments won't be entirely applicable)
Particularly this one:
http://jlcollinsnh.com/2012/04/15/stocks-part-1-theres-a-major-market-crash-coming-and-dr-lo-cant-save-you/The key point is, our guess is you're going to live another 40 - 60 years. The market will probably crash a number of times in your lifetime. But to the best of our ability to estimate, based on the last 100 years of boom and bust, war, depression, inflation and everything in between, it is likely that stocks will outperform cash by a decent margin. It will take time and experience, maybe some more reading, but you'll live a happier life if you can accept that the price of your stocks will fluctuate (although if history is any guide dividends in a diversified portfolio will fluctuate less).
If you're nervous it's completely valid (perhaps not statistically optimal but still often recommended from a behavioural perspective) to start with a slightly lower equity allocation and raise it over time/after you've gone through a downturn and you know (from experience) how you respond (i.e. if you can stay the course).
Your taxes are likely to remain well below the 28.5% mark soon so I'm not so sure about using a company.
In terms of investments, we don't quite have the range of options our US brethren do but we do now have a decent range of low-cost options. You're already on top of Cash/Term deposits available (although check out uBank with an automatic savings plan for cash) so you're mainly looking for equity investments.
Pretty much all the academic and practitioner evidence out there suggests that stock-picking, market timing, basically active funds management in general, won't (in expectation) produce better results than holding an equivalent index. So I use index funds and ETFs.
If you want to have more in Australian dividend-producing stocks there are now a few low-fee dividend-focused ETFs available (most of the ETF providers have one). I personally like the iShares one IHD as it caps the percentage in any individual stock as well as to any broad sector (for example, financials - mostly banks - are over 35% of the ASX200 but IHD caps each sector at 20%). I haven't yet pulled the trigger on it myself. You could then diversify further with, for example, a broader index ETF such as Vanguard's incredibly low cost VAS (roughly the top 300).
For International if you want to keep it simple there's WXOZ (Developed Markets ex-Australia) or there are lower cost options if you don't mind having multiple ETFs (in particular vanguard have VTS, which is the Australian cross-listing of MMM's beloved US Total Stock Market fund, and VEU which is developed world ex-US: full disclosure, I have holdings in these two). iShares have a variety of other funds if you want to slice and dice further (e.g. emerging markets, US Small Cap, etc.) but some of those options are a little pricey and you may be more comfortable starting with just a few funds.
If you decide to go the ETF route, when you're ready to start, do a Google search to find offers for free brokerage for the first ~10 trades or 2-3 months. For example if you search for "commsec $600 free brokerage" you'll find such an offer, similar for NAB trade and there are probably others. The nice thing for those of us who buy for the long term is once you set up your few ETFs you'll rarely need to pay brokerage - if you're comfortable you can do the bulk of your purchases with the free trades and you probably won't need to sell for a very long time.
I have some more options on my blog (including non-ETF funds if preferred) but I think those basic funds will give you a decent degree of diversification with rock-bottom expenses. If you have some super don't forget to include that in your overall high-level asset allocation (and there are sure to be low-cost funds available that can complement the choices you include in your non-super allocation). Hope that helps!