Hello, Glimmerman. Over the years, with the BHP, I've come to believe that "less is more." Years ago, I used to have about everything changed on the HP that I could and my gunsmith tried to tell me that some of my ideas weren't all that hot. I wish I'd listened.
Not from a collector's view of course, I believe that today's BHPs are the best ever in terms of what you get for your money and out of the box. You get very usable fixed sights which I prefer over the far-too-high adjustable sights currently sold. The bbls in my new MkIII 9mm HPs fit better than the factory bbls in my old '71 and '74 HPs; I had BarSto bbls fitted to them to tighten up groups, but do NOT expect the HP to group as tightly as a fitted 1911. Do expect them to do about 2" at 25 yards from a rest with loads they like.
Like many HP addicts, I eventually had plain black-on-black fixed Novak sights put on a couple of my HPs with the front sight blade purposely a tad high so that I could zero by careful filing down. I got them dead on at 15 yards which is about as far as I shoot anymore at targets due to my eyesight which just ain't what it used to be! On "good" days, I'll shoot at farther distances and it's almost like the good old days. Anyway, I had the sights added and after several comparisons learned that my groups were no tighter than using the factory sights. At speed, doing "practical" drills, hits were about the same in terms of "tightness" and time. The guns do look better in my view, but in terms of a real gain, no. (Of course, there's utterly nothing wrong with a good looking pistol, either.)
I'm one of the number who do get bitten by the HP's spur hammer. If this malady afflicts you, I suggest the following:
1. Either replace the hammer with the Cylinder & Slide abbreviated "ball hammer" or,
2. Bob the existing hammer at the second lateral serration, shape it to suit you, refinish and go.
I remove the right-side (as the pistol's facing away from you) ambidextrous thumb safety lever. The way my hand fits the gun, it can accidentally engage it.
While somewhat controversial, I do routinely remove the (hideous) magazine disconnect that prevents the weapon's firing without a magazine in place. I like a pistol that CAN fire without the magazine in place if need be and this generally cleans up the trigger pull in most instances, by an estimated 10 to 15%.
Some will counsel against this and there very well be merit in their argument, but to me, such a modification to a BHP makes it no more "dangerous" than the various makes of 1911s, Beretta 92s, Taurus PT92/99s, CZ75s, Glocks, SIG-Sauers, and so forth.
I replace the factory thumbrest stocks as they're not comfortable to me. If they are for you, no problem.
In the 9mm HPs, I replace the standard factory recoil spring with a Wolff conventional 18.5lb spring to reduce possible battering and I use the shock buff for the HP available from Buffer Technology,
http://www.buffertech.com in my pistols.
I realize that you're speaking of a .40 S&W HP and they have a heavier recoil spring than the nine millimeter. I might leave it the same, but I'd sure try the shok buff.
Myself and others do counsel against having the HP's front strap checkered due to its being rather thin and a checkered gun my crack in this area if dropped or even squeezed hard if the checkering's cut too deep or the particular gun has a particulary thin front strap. Stippling is OK and I personally think it looks better on the HP, but that's subjective. I currently use plain old skateboard tape and don't worry about it.
Stocks are a very subjective thing, but I like Spegel's checkered stocks, but have heard very nice comments on Ahrends and others.
One of the more useless things I had done on an old HP was to have the front of the trigger guard checkered for the then-popular finger-on-the-trigger guard hold that was all the rage. Didn't work for me and for few others I know. Save your coin on that...if it was ever even a consideration.
Numerous finishes abound, but for my use as I'm not unable to clean my pistols for extended periods of time nor use them under the most adverse of conditions, I usually opt for old-fashioned bluing.
IF you decide to go for adjustable sights, let me know and we'll go from there.
Best and good shooting.