I help you with Australia:

1. You'll need to check if your skill set/qualifications are listed on the Skilled Occupational List (SOL) or Consolidated SOL. If so, this will be the cheapest way for you to obtain a visa (subclass 189 - Skilled Independent or Subclass190 - State Sponsored. The difference between the 2 is the 190 requires you to stay & work in the sponsoring State for 2 years, whereas the 189 doesn't have any restrictions. Total cost (without agency fees) payable to DIBP is about AUD6000 (Visa fees, IELTS exams, costs of certifying documents and degrees, costs of getting everything non-English translated into English etc). Agent fees can easily cost an additional AUD3000 to AUD4000.

You will need to get your UK degrees certified as equivalent to Australian standards by EA (Engineers Australia) - and you'll need to pass a points test.

2. Is your wife a specialist? Where did she graduate? Depending on these factors, she might qualify as the main applicant, because I know that doctors are in demand in Australia right now (there's news in the wind to say that this might change in 2017). However, getting certification and an Australian Registration can be a nightmare with AHPRA, especially if she didn't graduate from an Australian or NZ school. It's all quite protectionist, I'm afraid.

Once you've sorted out your eligibility, lemme know and I'm happy to offer my further 2 cents.

No worries, I'm not a MARA (Migration Agent Registration Authority) registered agent - just somebody who've been there, done that and bought the T-shirt to boot. Three times, actually.