In a nutshell, NONE.

I grew up in cougar country and have never worried about having to protect myself from one. The number of people that have been attacked by cougars in North America in the last 150 years can be counted on both hands. Your odds of getting killed in a car wreck on the way to the woods is a lot better than getting attacked by either a cougar or a bear.

Besides, very few people can shoot a handgun in a high stress situation accurately. Anyone that has been in combat will attest to that. If I had my panties in a twist and was paranoid about walking in the woods I'd carry a pump shotgun.