I can and do carry my 4" S&W 629 when weather permits the style of dress that is conducive to concealing a large handgun (use of a jacket or coat as a cover garment). While there are smaller and lighter .44 Magnums available, my 629 (standard heavy barrel, not the tapered barrel "Mountain Gun") is the smallest and lightest .44 Magnum that I care to shoot with Magnum ammo.
For concealed carry of a gun of this size, I prefer an Askins style holster as it tucks the butt in nice and close to the body. I use a Kramer that I found in the used holster bin at my LGS for $6, but El Paso Saddlery's "Double Agent" is a very nice one and would probably be my choice if buying new (I bought one of the El Paso's for my dad to use with his 4" M29-2).
For ammunition, I currently use Remington Express 240gr SJHP. This loading provides me with more than ample power without overly punishing recoil. I also like the design of the Remington bullet because it seems to expand more aggressively than many other JHP designs for this caliber. Finally, the 240gr bullet is standard weight for the caliber and I don't have to adjust my sights to shoot POA with both my carry ammo and my 250gr cast practice loads. If you don't mind a lighter bullet, Winchester 210gr Silvertip and Federal Power-Shok 180gr JHP are also well-thought-of SD loadings for a .44 Magnum. Hornady's 180gr Critical Defense also looks promising, but hasn't been on the market long and thus hasn't established a reputation one way or the other.