Canuck, I recommend that you put a few hundred rounds through it before doin any changing. Unless you really know what you are doing...DO NOT REMOVE THE SIDE PLATE. I would suggest getting a copy of Jerry Kuenhausen's book on S&W revolvers and reading ALL of it a couple of times before trying to work on your new piece.
Sear engagement is almost always right to start with on the Smiths and more often than not, action work makes them worse. Just shooting most of them is enough to really smooth em out. Trigger pull can be lightned safely. Easiest and most effective is to lighten the trigger return spring. Again read a good book untill you know it well before changing anything.
I even recommend shooting it quite a bit before getting it ported. Especially if you are thinking of it as a defensive gun. There are some definate drawbacks to porting that, for me, offset any gains in muzzle flip. After all, tis not a rompin stompin cartridge....just a darn good one. I often carry a 3" 696. It is a tad smaller than your 625 and my .44special loads are in the upper level of .45ACP for strength. Stayin with moving target for multiple shots becomes easy with practice.
Welcome to the wonderful world of wheelguns.....enjoy.
Sam...follow me, I found a new way to get there.