I would check out the laws in your state for legal handguns to hunt with since you said you have a tag for a cougar. That may limit your selection of minimum barrel length and caliber []. I would like a 5 inch with a bull barrel in 357mag minimum. I prefer the 44mag but I shoot it alot [8D].
Make sure you practice drawing the pistol in a hurry and keep it accesible.
Good luck!!!