The fees for an application with no dependant children are $1040. That's what you have to pay to CIC. You can pay the Right of Permanent Residence Fee later on (it's $490) when the visa office is ready to issue a visa, but it's advisable to just pay upfront if possible, since paying it later will cause delays for your application.
And of course, there are other expenses you will encounter along the way, like the medical exam, mailing fees, the fees for putting all the evidence together,...
His parents can't sponsor you. The only way they can participate in this is to provide a letter saying you two will be living with them when you move to Canada. This is not sponsoring you, your husband is still the one and only sponsor. He will sign an agreement, promising to provide for you for 3 years. His parents would be under no such obligation. They only provide the evidence that he does indeed intend to move to Canada with you.
As Leon said, the job offer will be the perfect proof of his intentions. If he could get that, it would be great.
As for the evidence... there are 2 things that you need to prove with a common-law application.
1.) You need to prove the
relationship is genuine. For this, you include emails, photos, cards, boarding passes, wills in which the other is the beneficiary... Anything that shows you're really a couple. You need to do the same with a spousal application.
2.) You need to prove
you are common-law partners. For that, you have to prove you have been living together for at least 12 months. A lease in both your names perhaps. Mail addressed to both of you. Mail addressed to him or you at the same address. Anything that shows he has been living at the same place as you. If you were doing a spousal application, this wouldn't be necessary, all you would have to include is the marriage certificate and that would prove you're married.
I really have no clue on how to move cats across continents, hopefully the link Leon provided will be of use
