I have a South Australian accent myself. It's pretty much entirely self-taught with the help of learning the IPA and practicing pronunciation for years. I used to speak with a light Canadian accent when I decided I wanted to teach myself to speak Australian English, and in the process, I kinda made a pitstop at Cockney and accidentally forgot how to flap my t's. It's not really problematic, and it gives my accent a little idiolectic twist, but I am teaching my self to flap my intervocalic t's again.
As for the accents I like. Of course, I love Australian accents (kinda why I wanted to teach myself one). Broad ones are pretty awesome to hear, possibly from the years of religiously following the Crocodile Hunter when I was a kid. There aren't that many accents I dislike, to be honest. Most of them are either so ridiculous they are comical: such as the Lanky dialect or Yorkshire dialect, or are incredibly sexy and cool, like Scottish, Aussie, and Canadian. American accents kinda fall in the neutral zone with me, even though I love Mid-Atlantic accents, and Southie English kinda falls in the so ridiculous it is comical category. New Zealander accents are something I try to avoid (and sometimes fail at that) speaking. I've occasionally shocked myself with my pronunciation of words like fish and chips as fush and chups, and I've been frantically hypercorrecting that by tensing my i's even more than ever. Still, I don't dislike New Zealander accents, as long as I don't start speaking it myself.
The only kind of accents I strongly dislike are the half foreign half English accents, especially the Dutch version of English known as Steenkolenengels is lurchworthy whenever it appears within my hearing range. Most other foreign accents add an exotic tinge, but Dutch, no...no...just no.