118mm would be for a triple. I don't think 108mm is so common, I have a FSA Gossamer road dual which uses it and have not found 2nd hand 108 BBs easy to find, I guess MTBs don't use it.

So 113mm or possibly 108mm is the likely size. 113mm will be around for ages.

You can get some idea of the offset of your cranks by holding the BB end flat on a tabletop and measuring the height up to the side the pedal screws into. Road cranks have a total width of about say 155mm, so you can do the math.

If you keep your old crank, measure and check for an offset BB - it was quite common to have an offset of 3-7mm back then. Modern BBs are all symmetrical but a 1.5mm spacer gives you a 3mm offset which is usually near enough. The UN-55 with its metal LHS adjuster may be a better bet than the older plastic adjuster if you are going to run it with an offset.

Nearly all modern cranks will look a bit silly on an old bike, even the silver aluminium ones.
You can get longer old cranks. Over 175mm is very rare (in New Zealand at least) before the late 1980s. They appear in the catalogs since way back but the first real-life long cranks we see are Shimano 600 Ultegra FC-6400. and a few of the 105 FC-1055.
Suntour Superbe Pro are sometimes long too, though you have to fight the hipsters for them and they have an ISO BB.