Gday mate, good choice moving to this country you'll love it theres none better.
Bull arabs can do the lot, depending on the quality obviously, they often make top finders and holders, definitly one of the top all around pig dogs you can get.
Its easy to buy pitts in oz although they are illegal in some states and other states place certain restrictions on them.
Am bulldogs generally always make top luggers, but depending on their line or build they can sometimes be slow or be susceptible to heat problems.
Your last question is a difficult one to answer as there are so many breeds or mostly crossbreeds that do very well as pig dogs. Going by your questions regarding pitts and am bulldogs Im assuming you have an interest in these breeds, both are top dogs but can sometimes be a bit hit and miss as pigdogs when they are pure but both generally make good dogs when crossed. I have seen both these breeds crossed with bullarabs and the offspring have all gone on to make good pigdogs, just something to consider.
A good thing to do when you get to your new area over here is to take note or talk to hunters about the breeds or crosses that seem to work well in that type of country and make your choice on what dog you want to get then.
Anyway then good luck with it mate and I hope all goes well with your move.