Congrats MC92 on finally finishing the application!
Most definitely send it by courier with a tracking number so you will get confirmation once it is received by the Mississauga office. This is important so that you will have peace of mind and written proof to know it arrived at its first destination. If immigration ever makes a mistake - which they unfortunately do more often than they like to admit - you will always need documentation on your end to follow up and have them correct any errors.
Paying the fee does not generate a client ID (put a copy of the receipt in your package if you have not sent it yet). You should have gotten a message like this:
"Please do not reply to this message. Replies to this e-mail will not be acknowledged.
Attached to this e-mail is a copy of your official receipt for the payment of Citizenship and Immigration fees. Please print this receipt and attach a copy of the receipt to your application.
Your case processing centre will only accept a printout of the official receipt as proof of payment. Thank you.
Citizenship and Immigration Canada Government of Canada"
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You will not be given a client ID until CIC Mississauga logs your application into their system. If you have used an e-mail address for your contact CIC will e-mail you when it gets logged in and that e-mail will contain your Unique Client Identifier or UCI number along with your application number. Once your sponsorship application gets approved (SA) they will then send another e-mail with a letter attached. Not sure what the timelines are like now (they are posted on CIC's website though and updated every quarter) but when I submitted our application on Feb. 7, 2013 we received our 1st email, UCI and application number on Feb. 20, 2013 and SA on March 28, 2013.
This part of the process happens relatively quickly. Once the file is sent to the visa office (VO) overseas though, is when your real waiting will begin. So be prepared to be very patient for that part as it will test and try you as individuals and as a couple. Blessings for a speedy approval.