The 3" K-frame revolvers (M-10, 12, 13, 64, 65, etc) are about as perfect as a personal defense handgun gets. I have owned a 3" Model 10-HB for over 30 years, and I can't imagine anything that would be superior for every day personal defense use.
That said, be careful about expectations for ammo performance in the shorter barrels. Published muzzle velocities and energy are not likely to be attainable with the 3" barrels. Even if you can achieve the claimed MV and ME ratings you will probably subject yourself to excessive recoil, muzzle blast, muzzle flash, and other trauma. I recommend ammo in the .38+P range, and only when proven to shoot to point of aim in your revolver (most fixed sight revolvers are factory regulated for standard velocity loads of the most common type; i.e.: 158-grain RN or SWC, and other ammo types may demonstrate wide varieties of POI in relation to POA).
For carry purposes there are two primary considerations:
1. Concealment is the priority. In this case a good pancake-style holster worn just behind the strong-side hip (3:30 to 4:00 position) is recommended. Suggest you look at the Lobo Gun Leather 'Enhanced Pancake Model'.
2. Accessibility is the priority. In this case you might consider the Lobo Gun Leather 'Combat Classic' model, reasonably good concealment with outstanding accessibility.
Full disclosure: I am the founder of Lobo Gun Leather (1972-2015) and now retired, serving as a consultant to the Fedders family now producing the designs I perfected over 43 years in the business.
Being a consultant means that I have to shave more than once per week and dress better than your average homeless person. Maybe I also know a little bit about handguns and carrying them.