The exact model of crankset is the main determinant of what bottom bracket is best.

1980's Pinarello will of course be Italian-threaded, and Shimano does make a good variety of bb's with Italian threading, but the taper is slightly larger, so the cranks don't go quite so fully onto the spindle ends.
The original bb is also possibly offset, extending further out on the right end, so this will figure into the length requirement of any replacement.
Also your frame will likely have more or less chainring clearance than other frames, which may need to be respected if you use a different bb.
The final "chainline" (offset of the chainrings away from the center of the seat tube) can be biased inward somewhat in many cases, which can improve the running angle of the chain if you like to use the full range of rear cogs while using the large chainring. This is the way I prefer to set them up.

As you can by now tell, this can get complicated. Many will advise using only original parts, but I have many times been able to get a Shimano bottom bracket to fit well and work well over the long term. The trick for me has been doing a test-fit or two using available cartridge bb's that I have at hand, which allows me to home in on a minimal chainline dimension that works on a particular bike. It is also acceptable to use fixed-cup spacers to bias the chainline outward, if the chosen bb turns out to be on the short side, which may be the best for you as it often has been for me.
Since I never use the small chainring with the smallest cogs, I don't worry about having the chain running clear of the big ring when in the smallest front and rear sprockets, so a shorter-than-original spindle causes no problem for me.
Remember that a Shimano bb spindle will space the crankarms about 4mm further apart overall than will a same-length Campagnolo spindle, because of the thicker tapered sections. That translates to two mm per side.
There are also "ISO" bb's that have an even smaller taper, equivalent to about 3mm per side narrower than a Shimano spindle or 1mm per side narrower than a pre-cartridge Campagnolo bb.
A cartridge-style Campy bb will be ISO taper, so may act a couple of millimeters shorter than any earlier Campag bb of the same overall length.