Welcome to the forum!
Taiyo Yuden's the manufacturer, and Plextor was just one of many brands of Taiyo Yuden disc (Plextor media is not sold any more IIRC) - but TY discs can be found under many other brands. Brands can differ, depending where you're located, but in general look for "Made in Japan" on the packaging.
Re: your link. Being in the UK, I've never used that store, but maybe someone in Aus can help out.
One thing about it that did strike me as odd - the item listed is named in several places as "Taiyo Yuden CD-R" - however, scroll down a bit and it says the media code is TYG03? That media code is for 16x DVD-R.
So either that's a genuine typo on their part, or they don't know what they're selling
As for burning programs, I use either Nero 8 or Roxio for general burning. Other folks will have their preferences, too.