My choice would be the Hornady .44 Special Critical Defense ammo. Plenty of power, excellent bullet, designed for short barrels, low muzzle flash, easily controllable and takes care of the over penetration issues.
http://www.hornady.com/assets/files/Critical Defense-Personal Defense Breakthrough.pdf
My choice of ammo for my .44 magnum is the Hornady loaded with 300 grain XTP bullets which I use for both self defense and hunting. For anything bigger than black bear I use the Garrett ammo ( www.garrettcartridges.com ) which is the best of the best in the +P and +P+ .44 magnum ammo. The handgun you show here is the choice of Alaskan Wardens loaded with the Garret ammo and they also carry a 12ga shotgun loaded with slugs. I have a Gary Reeder ( www.reedercustomguns.com ) custom built Kodiak Magnum which starts life as a Ruger Super Blackhawk and then he works his magic on it and it is the finest hunting handgun in .44 magnum for me. I feel that Gary Reeder is the premier pistol smith in the business today and Randy Garrett is the premier ammo maker of the .44 magnum and the 45/70 out there today as well. The Garrett ammo is only loaded in the .44 magnum and the 45/70 using his patented Hammerhead bullets which are what makes his ammo the best of the +p and +P+ out there. When you combine the handgun of Gary Reeder using the Randy Garrett ammo the combo is unbeatable for both self defense and hunting today. I would suggest that all visit both of the websites I listed and be sure if/when you visit Randy Garrett's site to visit each item in the site menu as they are loaded with great info. Please note that when I post I always post what is my opinion and it is meant as simply that, my opinion and nothing more nor less. I spend time on a couple of other sites where I try and use my knowledge and experience to help my fellow gun lovers and hunters.