Just a bit of info in regards to trigger pull, especially on the models that were one commonly Police Duty pistols. Police Dept. Aromorers have been tuning on the S&W revolvers action since it's introduction and because these guns were mainly used in Double Action, that is the area that they worked to optimize. A consequence of any work to lighten the DA pull will also reduce the SA trigger pull. So, it's not uncommon to find a lot of these guns with light SA triggers.
One typical action taken was to shorten the rebound spring by 2 coils. This takes the "weight" of the rebound spring down to about 14 lbs. The result of doing this is a DA trigger pull in the range of 8 to 8 1/2 lbs. and a SA trigger pull in the range of 2 1/2 to 3 lbs. For many shooters that can seem a bit light.
The next thing that was typicaly done was to file the strain screw down by a small ammount, probably 0.010 to 0.020 inch. Doing this will allow the strain screw to be fully seated but it will put less tension into the mainspring. It will also further reduce the DA trigger pull to the range of 7 1/2 to 8 lbs. At the same time, the SA trigger pull will drop to a bit less than 2 lbs, which is enough to produce a trigger that feels "light as a feather".
If you want to restore your model 19 to "stock", it's pretty simple. What you will need is a new, stock rebound spring with a weight of 15 to 16 lbs. and a new strain screw. By installing these parts you'll have a DA trigger pull of about 10-11 lbs. and a SA trigger pull of about 4 lbs.
If you don't want the DA pull that heavy, install a 14 lbs. rebound spring and that new strain screw. This will produce a DA pull of about 8 1/2 lbs. and a SA pull of slightly more than 3 lbs., which IMO is just about optimum for a S&W revolver.
PS, don't neglect getting a new strain screw for your model 19, I am almost certain that you'll find that it's been shortened and putting a shim between the strain screw and the mainspring is a temporary patch that may not stay in place. In addition, a shortened strain screw could cause problems with achieving proper tension with the mainspring and that can cause problems with misfires. Fortunately, this is NOT an expensive part and it's easy to get. Following are links to this screw on Numrich's site for both Square and Round butt model 19's.
Strain Screw, Square Butt, Blue
Strain Screw, Round Butt, Blue
Pss, note that I do NOT believe that you need to replace your mainspring. When your model 19 was produced it wasn't normal to replace or modify mainsprings because it was so much simpler to just grind a bit off the strain screw for the same effect. IMO, the only parts you need are a new rebound spring and a new strain screw.
Added, link to rebound spring selection kit's from Brownell's. Unfortunately, I did not find a good selection of strain screws on Brownell's web site, so that would have to come from Numrich's. However, Numrich doesn't seem to carry the Wolff rebound spring kits, thus the link to Brownell's offering. Yeah, it means paying shipping and handling from 2 sources instead of one, but it's a workable solution. At the same time you can find the S&W revolver manual on Brownell's and the Rebound Slide Spring Installation Tool, which is an absolute essential for working on these guns. I would suggest getting the Manual, Rebound Slide Tool, and the 9 dollar (1667) spring kit from Brownell's and perhaps seeing if your search skills are better than mine, they may have the strain screw somewhere that I couldn't find. All told it will cost less to do this yourself and it's not at all difficult, just make sure you read the manual on how to remove the sideplate, IT CANNOT BE PRIED OFF WITHOUT DAMAGING IT. It can also be a bit fussy getting the sideplate back on the first time you do it, took me 40 minutes the first time, now it takes less than 30 seconds because it's a "feel" thing you learn. If you run into a roadblaock getting the sideplate back on, do NOT force it, just ask in the Smithing Subforum for tips, we'll guide you in.
http://www.brownells.com/.aspx/pid=16530/Product/S_W_REDUCED_POWER_REBOUND_SPRING
http://www.brownells.com/.aspx/pid=774/Product/S_W_REBOUND_SLIDE_SPRING_TOOL
http://www.brownells.com/.aspx/pid=25717/Product/THE_S_W_REVOLVER___A_SHOP_MANUAL