Hi Cowboy...
Don't do a thing until you've dry-fired between 1000-2000 times. Three things happen: the springs settle, the parts smooth out, and your muscles get stronger. You probably know this already but it bears repeating for those who may not.
In a span of a couple of months last year, my wife got a 642 and I got a M&P340. Our first revolvers. The springs on her 642 seemed lighter than my 340 and her action also seemed smoother - fewer felt rough spots. These were to be "last ditch" defensive carry pieces anyway and before buying, I did expect stiff triggers. Better too stiff than too light.
After lots of dry-firing, both pieces loosened up - the rough sections diminished and the springs seemed loss stiff. During the dry-firing exercises, I mostly did two hand and right hand intentional quick follow-through which is most likely how I will fire it if faced with a threat that justifies deadly force.
But I also did slow pulls. When you do it slow like this, you will hear/feel the first click, then the second click. At the second click, stop. This is the shelf. Any farther and the hammer is released. (my 340 had a bit of roughness at this hammer release point) Slow pulls develop muscle and build control.
By dry-firing, I got good at a medium-quick pull and stopping after the second click, exacting my aim and firing. Stopping at the second click is almost like pulling the hammer back and firing in single-action.
Of course, that type of drill is for more accurate, deliberate longer distance shooting where you have a second of extra time which is not what these little guns are for. Almost all of my practice with the MP340 is quick, smooth, aimed complete firing at ranges of 5-10 yards.
I look at indoor dry-firing as training and I even use a target.
So anyway... after this break-in period I did want to open them both up to get the metal dust out and since I knew I would have them open, I figured I would learn a new skill so I bought two Arkansas stones, watched the Yoda-G video about 10 times and found a S&W exploded J-frame diagram.
Both revolvers got a thorough interior cleaning and careful polishing of the contact surfaces and judicious, selective lubrication. I replaced the 18# (?) trigger rebound spring in my wife's 642 with a 13# Wolf but left mine with the factory rebound. I left both factory hammer springs, too. It went well. The only mishap was losing the smallest spring (sear spring) in mine and I had to vacuum the room with a stocking as a filter to recover it.
Both are now ultra smooth, the 642 which had a lighter pull anyway is more suited to her but I left my MP340 on the stiff side which I prefer because if I ever have to use my .357 when it counts, I won't be concerned with the trigger pull.
Good luck with yours.
Oh... .357 ammo through the 340? I don't advise it without a thin leather shooting glove. You might want to try it so you know what it feels like - it's fun but the hard snap is enough to move skin at the bottom knuckle of the thumb. *thin leather glove*. If you want performance between .38+P and full .357mag, I found that Buffalo Bore 19G/20 125JHP is shootable in the j-frame and is designed to be low flash, quick burn and reduced recoil. It's what I carry.
The trigger pull was...stout. 
The $26.95 I paid for the Apex Tactical Duty Spring Kit was more than well worth it. 
