Cups with pitted races are toast-- the spindle may spin marginally smooth after repacking but the pitting will only worsen with time. Time to replace the cups or just upgrade the entire BB unit with a modern cartridge unit.

If you really want to maintain the original spindle (provided its races are in good shape) you can just replace the cups for about $20/pair (check amazon). But for just a few dollars more you can get an entire cartridge unit that'll spin like buttah (look for a Shimano UN54 or UN55)

As for size of BB to replace it with, if you intend to keep the same cranks, order a BB with the same spindle length (measure end to end not including the crank bolts). However, the original spindle is likely offset to the drive-side by a couple of mm, whereas a cartridge unit will be left-right symmetrical. In this case, get a 1-2mm spacer to space out the cartridge unit to the right.

Good luck!