I have heard (on here) it can be up to ten grand if the mother has no health coverage. It will vary by province. If you are a Citizen by birth your baby will be too no matter where he or she is born (just in case wanting to have the baby here has anything to do with that).
It's a job and a half to gather/organize/fill the documents. FBI reports take some time I have noticed.I didn't deal with the US so I don't know all the specifics.
You will need as much proof of your relationship as you can get. Bank statements/rental agreements (showing both your names) anything that shows you have combined your life personally and financially. Mail to your address for each of you. I assume you will apply as common-law(you said wife to be), you have to have resided together for a minimum of 12 months. Letters from family and friends are great to include(I think they are asked for in common-law applications), Facebook walls, emails, travel together, tickets to events...ect.
Read the forms and the guides, get a good feel of what they ask and or need. It can be confusing to say the least! I suggest also to print the forms, then fill them in by hand as a template before filling them in on the computer. The forms will only allow for revision so many times and then you would have to re download it and start over. (pain in the...fingers)
If you run into problems or questions there are plenty of helpful people here.
Congrats on the pregnancy!
Take care
MadeInCanada