Ex shop mechanic ramblings:
Being that cottered cranks are indeed a 'dead technology' I don't have a ton of experience on them, however, I have ridden a few bikes with them. One thing that seems to be critical is that you use new pins when installing them, or at the bare minimum ones that are in very nearly new condition. the other issue that will come up is if they do come loose, and you continue to ride it, you'll probably destroy it. On a cottered setup if it is not too bad you might be able to just fix it with new pins. Once you round out the flats on the axle even a little bit, the axle and the pins are trash. If you feel any play, the correct course of action is to stop immediately and tighten things up. The square taper ones are often ruined this way, and bike shops deal with this all the time. If it is properly torqued down in the first place, it won't come loose, but that doesn't always get done. If you ride a square taper while loose, you can ruin it within a matter of blocks, even without standing. This ruins the arms but not the axle, as long as the arms are alloy. If the arms are steel, it will probably ruin both. Make 3 piece setups TIGHT. if you strip the bolt head, that's too tight. slightly less than that is about right.
The 3 piece BMX cranks with the 48tooth spline 19mm axle and tubular cromoly arms are pretty much indestructable, and (I think) will also accept your vintage chainring of choice. Last I checked they are about $200 though. the cheaper BMX versions with a pinch bolt can be hit or miss on quality, but likely ok for rat-rod purposes.
bending a 1 piece is fun... it's like having suspension ..... for 1 run. you can bend it back with a vise and a big pipe over the other end... and then don't hit any more jumps. 1 piece is the "correct look" for most of the bikes around here, and it's fine if you're not jumping. The bearings aren't the greatest, but they'll do.
As a mechanic, I would not hesitate to run any of the systems out there (on a rat anyways). Having said that, the 1 piece is probably the least hassle. If you have an english BB (aka threaded) a modern sealed bearing BB and a square taper crank is the least hassle/money. If you have some cash to throw around, a BMX crank is probably the highest performance, and is available for either BB type. 1 piece is not all that heavy (lighter than the good BMX stuff actually). Alloy armed 3 piece off a modern mountain or road bike is obviously the lightest.
By the way, the correct way to remove a 3 piece arm(square taper) is with a puller that threads into the arm.
my $.02....