They did use solid silver cases, just as they used solid gold - but plated-over-brass or 'gold-filled' and 'silver-plated' were common - as were nickel-plated versions.
Chrome was unheard of.
Watch fobs were used with vests all the time - even with chains, since they were a convenient way to retrieve the watch from the pocket.
For SASS - use a quartz movement, and don't spend much.
For NCOWS - use a period watch like one of the more common Elgins or Walthams - they're tough and they'll keep time, and they made a lot of them, so finding a good one should be easy, since they're all over ebay and in all of the antique malls.
They'll also keep time well, once you train yourself to wind them regularly.
As for that - the cheap little battery-powered watches you can buy at the checkout line will keep better time than my Rolex Sea Dweller - but no one cares about those...
Going back to fobs and chains - your station in life will determine whether which one you'll wear.
If you're a townsman - a chain would be common, but if you worked outdoors, then a fob, since your manner of dress would dictate hardier clothing than that of a townie who wore a suit.
Scouts Out!