While it is not a Herculean task to get a visa, it is by no means easy either. If you go to a decently ranked school, finding a job will be considerably harder than finding one while attending a top 10 university. And the question is extremely subjective since its the discretion of the employer, and not the school to grant you the visa. Most F1 visas come with an OPT/CPT period where you can work without a H1B. I'd advise you to think about the kinds of companies you want to work for - if they're multinational corporations, then the chances of you getting a visa are higher, but the competition for a job is over-the-roof too.

I cannot comment about Australia as I have no idea about the visa status there.

From what I hear after obsessively stalking the net for such info over the past year. Here is the summary of my knowledge in the matter:

1. The most frequent sponsors of the h1b in US after an MBA are the consulting companies especially MCk,BCG and Bain
and the Investments Bank Bulge brackets ( i.e JPM, CS, GS, etc...)

Although the job market for an international to enter IB is relatively difficult without a previous finance background, it is not impossible; while for consulting your previous background doesn't really matter. ( I have a professional mountaineer friend who went to BCG after a US top 5). In fact the more diverse the better it is for Consulting. It just might get you an edge in the IVs (though a previous analyst stint wouldn't hurt certainly).

2. On the other hand, Fortune 500 corporates are reluctant to sponsor h1b to the internationals and hence reluctant to let you past the IV stage. Even when you do push past an IV, you may have to sign a contract to get back to your geography after an international rotational program.

3. Like whiplash said above, The ManCons and IBs arent prone to recruit outside the M7 schools. So I guess you have more than a decent shot of securing an H1B out of an M7, while other schools may certainly be good enough in their own respect ( like Georgiatech's supply chain and industrial management) but the chances of securing an H1B is certainly bleak after an MBA from there.

No clue about Australia, sorry.

Again all my views are constrained without first hand experience. Hope this helps.