Smith and Wessons tend to have the best trigger pulls.
A nice tight used S&W Model 66 would be a good revolver for you to cut your teeth on. It is a .357, so you can use .38 special loads in it.
Personally I prefer 4" barrels on my K frames. In order of size Smith and Wessons go:
J Frame- concealment revolvers (snubs, etc.)
K Frame- used to be the "standard" size frame for .38 caliber (.38 Special and .357 magnum loads).
L Frame- created to provide a revolver that would stand up to constant use with .357 loads).
N Frame- the original "magnum" frame.
Why K frame instead of L frame? Personally, I don't shoot as many magnum loads as I thought I would over the years. I shoot .38 special loads a great deal and .357 magnum loads on occasion. A 4" Model 66 is a great packing pistol.
If you are hell bent on a .44, then there are three that I would take a look at. The Dan Wesson would be tops on my list. It is comfortable to shoot with full power .44 loads and they are accurate. You can still find them for less than $400.00 used. You can play with changing the barrel length, but unless you intend to hunt with it exclusively I would go for a 6" barreled version.
The Ruger Redhawk is a good stout revolver. Rugers do not tend to light me on fire, but there is nothing wrong with them.
The Smith & Wesson Model 29 (or 629) is a good packing gun. It is pretty light for the power it offers. A 4" has some real snout to it in the recoil department- and some of the factory grips they came with over the years may leave you not so happy after a range session. I would get a set of grips for the Smith that don't beat up your hands too much.
I would recommend you purchase a used revolver. Take your time- none of these things are rare. Learn to recognize the signs of a revolver that has been ridden hard and put up wet- these signs are more subtle on a stainless revolver- and be CHOOSY. Personally, I shoot my revolvers in double action mode most of the time. The quality of the DA pull is really important to me, and that is why I have tended to gravitate towards S&W products. The triggers on them can be tweaked into
mode.
Enjoy your new rig!