Did I hear 10mm?
This is ironic, as I've just been going through all of my resources regarding the 44 Special and 44 Magnum. (Resources being my two dozen or so loading manuals and the complete Handloader DVD set on the laptop.)
I've been loading 44 Magnum since 1983, and for the first five years or so, I looked upon the max loads as "a good start..." For the last 15 years or so, I've come to look at the S&W Magnums the same way as was written up in an article in Handloader mag. a couple-three years ago. I tend to treat them like large-size Model 19s - shoot mild loads 95% of the time, and warm loads <5%. It's easier on the guns, and on me!!
I started with the 44 Special in a single-action in the late 80s, and it was the only gun I had in the caliber for many years. Now I've got an 1866 and a snubbie to go with it. There's always been a lot of Keith-ish "the 44 Spl. is handicapped by it's anemic loadings by the factory" stuff about, and it is certainly true the Spl. can be "upgraded" by judicious handloading. (The best reference I've come across for this is an article a few years back in Handloader that groups most 44 Specials ever made into one of three groups, depending on the pressures of loads they can take.)
Having been in LE for 20+ years now, and trained on combat-style shooting, I know I would not want anything to do with heavy bullets in a 44 Spl. nor full-power Magnums for self-defense. Are they powerful? Sure, but there is no guaranteed one-shot fight stopper, and bullet placement (just as in hunting) is key. I can show you pictures of a guy that took a 44 Mag 240gr JHP full-power load to the face (bullet missed the brain), and lived long enough to walk almost a block away. If he was equipped with a weapon, he could have done in the 44 Mag - wielding shooter... No one who has recommended full-power loads or heavy bullet loads has ever shot combat-style. They're thinking of hunting and Elmer. Great guy, but his needs aren't the be-all, end-all for every purpose you need a gun for. Heavy bullets at medium to low velocity are still going to recoil more than light-to-medium weight bullets at medium velocity.
The main difference with hunting is that in self-defense, you don't poke a hole with a heavy SWC through the heart/lung area and watch the critter bound away and find it bled out 50-100 yards away. In a S-D situation, you want multiple-shot capability.
I think the original poster and most of the responders here get that, having read what they want and like, respectively.
The 44 Special in a factory load (what the OP said he was going for) is going to be a relatively low-velocity round, even if you find a lighter-bullet load. Personally, I'd prefer the nearly-pure-lead Federal 200gr SWCHP +P load that ran about 900fps, but I'm not sure Federal still makes it. That was probably the best SD load ever for the 44 Spl.
I don't believe there is any jacketed bullet (except maybe the Gold Dots that are geared for low-velocity expansion) that will reliably expand at the velocities you are going to get in factory ammo in the 44 Spl.
There may be some other vendors out there, like Georgia Arms who make a similar light-to-medium weight pure lead SWCHP load. If not, there should be.
Boiling it down to one sentence: Medium-weight bullet (200-210grs) of soft construction (pure lead or near to it - think swaged, Nyclad, or thin-plated Gold Dots) at medium-velocity (800-900fps) is ideal in the 44 Special. This will get you good terminal performance with relatively fast follow-up shots and less worries about over-penetration (but they still will probably go all the way through...).