170161 id the Performance Center version, about 100 dollars higher than the 625 JM and it's packaged with the ugliest grips to ever be mounted on a handgun.
IMO you should just get the 625 JM, it is actually a pretty well balanced package.
However, I found the JM grip to be too small for me and didn't provide the traction of rubber so mine is equipped with the 500 Magnum monogrip. Fact is that I like the 500 Magnum grip so well that one is mounted on every revolver I own with a round butt grip frame.
Pluses for the JM. A huge plus is the barrel features the quick change sight base, so if you want to swap in a fibre optic front sight it's a 30 second swap. Another big plus is that gold bead Patridge sight it's shipped with, it's a sight that IMO works well in a much wider range of lighting than any other type of sight. A minor plus if you are into it is that it features a Forged Trigger, something that I personally don't care a bit about.
Minuses. That Forged trigger is serrated and those serrations are sharp enough to draw blood from the most caloused finger. You will absolutely have to remove the trigger and stone those serrations down before shooting it or wear gloves. Since I find the MIM components to be just fine I installed a 0.400 wide smooth target MIM trigger in my 625 JM. The finish. That bead blasted finish has proven to be rather delicate and it will readily show rub marks. Once mine starts to look a bit like a beater I'll just wet sand the gun and then give it a full polish. I'll probably lose the laser etched JM on the sideplate but I just don't care, I bought it to be a shooter and it's a lot easier to touch up a full polish than a bead blasted finish. Final minus is the rear sight, for me it's totally invisible at the one local range that allows me to shoot rapid fire drills. It's made me a better point shooter but I wish someone would make a gold or chrome bead rear sight blade.
Cost. One tip is that if you are shopping locally to find a shop that will give you a discount for paying cash. Smaller retailiers end up paying big fees on every credit card transaction so many times paying cash can save you real money. Downside of this is that you'll probably have to order it in, so no looking in advance of the purchase. As a result if you get a canted barrel it's either a trip back to S&W or having a local gunsmith correct the cant on your dime. I ordered up my 625 JM through Sports South and it arrived in less than a week and by paying cash my cost before taxes was 800.00, with Michigan getting it's 6% it was 848.00 out the door.
BTW, mine had a rather badly canted barrel and I used that as an excuse to purchase a frame wrench. Then I took the 625 into the machine shop at word, removed the barrel to apply a precision crown and lap the forcing cone. After that was done I then re-installed the barrel on the frame while paying careful attention to getting the alignment dead perfect. Now I have to drift the rear sight about 0.025 right of center to zero it so it's apparent a slight bit of cant in the over tight direction is needed to perfectly center the rear sight. However I'm not going to bother doing that, when you start getting that barrel into perfect alignment it takes a LOT of effort to move it. Sometimes close just has to be good enough.