Ok ok ok... one Call of Duty reference is funny, two is kinda cheeky, but lets remember that this question is on a lot of newbie's minds.
No, you cannot purchase and use your own personal weapons in the CAF - you use what is issued. Most small arms (SA) is issued based on trade, position and necessity. As a general rule (I say general because a CO can change this on his or her say-so) 9mm pistols are issued only to a WO or above. C7 (as medicinman states) is our service weapon. As far a "variant" is concerned, we use the C7A2. The old C7 with the carrying handle has been phased out.
Some trades never actually get issued a weapon. We get one to qualify on the range once a year if we happen to be on a base where a range is accessable. Other times we actually do the COD thing (kinda) and shoot on a simulator. Enjoyable, however NOT the real thing.
If your position requires you to train with a weapon, upon clearing into your unit you are given a rack number. You draw your weapon for cleaning and maintenance, TOETs, weight bearing marches, ranges and training (exercises and stuff...)
Most of the older sods here this is second nature to, but we must remember that there is still a little "sexiness" to what we do and civilians and the like are curious.