Richard,
I have moved from Australia to the USA, and have gone through the visa process... just about to embark on the green card process. Would have loved advice when I went through it!
To answer your questions, you can be sponsored by a company as long as you have a University degree (called an H1-B Visa). This is probably the easiest way to get started. Once you are here you'll need to get legal advice on the best way to secure a green card.
There are limited jobs available. I know a few Call Center Management recruiting agencies that may interest you.
Feel free to email me with any questions you have:
gghavala@ford.com
Regards,
Gethryn