mynetfone are just one of the budget Voice Service Providers (VSP) that have a variety of VOIP plans. I have used them and found their service pretty good. I also use Pennytel, now, as my prime VSP as they are actually cheaper. MNF is my backup, along with the service provided by my ISP, Exetel.
I have used VOIP exclusively to make calls for several years.
You do not need any special software (that was for things like Skype and Netmeeting where both parties had to have the same). You can make and receive calls, though using a softphone Eg X-lite. This is often good for laptop with a HSPA connection for VOIP on the go.
At home, if you use software you will need to be tied to the computer, either via USB handset or microphone / headset combination.
The most flexible way is to use hardware. An ATA is an analogue telephone adapter and plugs in to your router. Som all in one devices have the modem, router and ATA built in (Eg Billion 7404VGP).
With a hardware setup it is good to ensure you router has a Quality of Service (QOS) function built in. This will enable you to adjust settings to ensure perfect voice quality while doing other tasks via your internet connection (browsing, downloading etc)
What you were talking about being able to receive Telstra calls is called PSTN flow through. It is also handy to have PSTN fallback, which allows PSTN calls to be made it the internet is down.
You can certainly set up the ATA to both make and receive calls via either your PSTN number and DID via the same handset. I do this with a cordless base station plugged into the ATA port.
A term you may have read is dial plan. This is what you input to tell the ATA where to direct which calls. THis is used for lowest cost routing. Eg one VSP has low rates to Australia. Another has the lowest rates for mobile. And a third has lowest rates to the overseas country you call most. Via the dial plan you can tell the ATA which ISP to use for which call type, automatically.
Ok, so that was a lot of info without too much depth, sorry, but there are a few ways to get things going.
Simplest is to order a preconfigured device from a provider, however these are sometimes locked and may be inflexible. Most flexible is to order an unlocked device from any IT retailer (Eg jmgtechnology or warcom) and input your VSP details.
There is a good wiki at Whirlpool (
http://forums.whirlpool.net.au/forum-replies.cfm?t=514445. Incidentally MNF have better plans and rates for Whirlpool members (
https://www.mynetfone.com.au/whirlpool).
Other good info is at
http://ozcableguy.com.au/voip.asp
Thing to remember: many VSPs provide a no join fee, no minimum spend, no contract plan. This is a good idea before locking in plans and contracts so you can try out VOIP and work out your call patterns to see if a plan would suit or not.
Good luck...
EDITED TO ADD: to answer your specific questions:
Yes anyone can call your DID or PSTN (Telstra number) from a normal phone.
A Softphone is needed only if you don't want a hardware solution. It is independent of VSP. It is independent of the 'system' the person you are calling has.
Plans: Pennytel:
https://www.pennytel.com/call_plans.html Free Access Untimed
MNF:
https://www.mynetfone.com.au/offers/whirlpool/whirlpool-plans/whirlpoolsaver-plan/ (I used the BYO because I had an ATA)
Exetel:
http://www.exetel.com.au/voip_planA.php Plan B