I'm in Perth, we moved here in 2013. I concur with most of what is said above. We bloody love it here, we have a beautiful house near the beach that is fairly cheap as its small by aussie standards (but huge and lovely compared to anything I lived in in the UK). I absolutely adore the long hot summers, and spring and autumn are pretty nice too (although I wish this spring would bloody HURRY UP). Winters are mild and short and a bit dull as everyone hibernates (or pisses off to Bali). I do think I would have found it a bit dull in my 20s, but then I lived in London in my 20s so not really a fair comparison. For families, in my opinion, its paradise.
There is a slow down at the minute, depending on your profession this might affect you. Its bloody hard to get a job before you get here, but do if you can. it is expensive until you are working, when you are still converting everything back to stirling in your head the prices will be horrific, but you get used to it, and in my opinion it is far easier to have a great lifestyle on an average wage than it was in the UK.
You will need a car straight away, distances are much bigger here. I disagree that public transport is crap, if it goes where you want it to it is cheap clean and efficient, its just that it cant possibly cover everywhere. FWIW I dont drive, and I work full time, I get to work on the bus just fine (and I dont work in the city).
One thing we have found is that the people are lovely. We started out with making fellow pommy friends, but now know loads of people Aussies, Kiwis, South Africans etc. Lots of people choose to live in very pommy places (Secret Harbour, Baldivis and Joondaloop, I'm looking at you), its really up to you. Familiarity is comforting at the start that's for sure!
What else? I recommend air con for summer and a log burner for winter, winter here is freezing because of the stupid uninsulated houses.
As for culture, this is plenty there if you want it. This year I've been to see Little Shop of Horrors, Picnic at Hanging Rock and The Sound of Music (last night! was fab!) at the theater. Its never going to be London, but unless you are a dedicated culture hound, there should be enough to satisfy you. But that;s not really what Perth is all about. Its about getting outside, going to the beach, having a barbie with friends, playing or watching sport (I hate it) enjoying the beautful wildlife (dolphins in the bay, fairy penguins, kangaroos, kookaburras), chilling out in the sun with a beer! if that sounds like your kind of thing, you'll love it. Good luck!