I am rebuilding my old 1987 Schwinn Super Sport. The original bottom bracket (cup and cone style) are basically no longer available so going with a cartridge style is the only practical and cost effective method. (Realize you could easily clean the old BB and replace the ball bearings, but it'll be hard to find spindles or cups/cone for it).
You've already figured out half of the specs: 68 mm width.
Next, you'll need to measure the overall length of the existing spindle, or often the length is marked on the spindle.. Note, the Sugino BB pictured says 103mm and 68mm, and this is shorthanded to 68x103.
Two other dimensions are critical, the threading and type of crank arm taper. Seeing you have a relatively common bike, the threading and taper fall into the 98% category.
Regarding threading, see and scroll down to "bottom bracket":
http://www.sheldonbrown.com/gloss_bo-z.html
You'll also need a bottom bracket tool to interface the cartridge. If you want to know a bit more, see and scroll to Bottom Bracket Tool Selection
http://www.parktool.com/blog/repair-...ottom-brackets.
And there is always a hot debate of whether to grease the spindles before attaching the cranks. I do, but some warn against it. It becomes a lively debate at times.