Here, in Canada, you can use your own serial numbering system. But it is supposed to consist of five digits, ie: numbers and letters in any combination. So a suggestion might be your date of birth plus a number or letter to indicate the sequence. I would stay away from social insurance numbers...they are private and should be guarded.
That being said, only handguns fall under the above numbering system. A longrifle can simply be the sequential number of the build. It is simply a number to identify that particular rifle, and together with photos, in the event of loss, is all that is needed by police or insurance folk.