Would like to easily look through old rims and bikes for sale and know rim width. Is there a chart that matches rim width to bicycle models, 12c-17c?

I'm afraid you are looking at a two-step process at best. First look up the catalog for the bicycle in question to find out what rims came with it. Then search the internet for information on the particular rim. I know there are a couple databases out there for current production rims but don't know of any for older rims.

However, the process I have outlined above can break down in any number of ways:
Catalogs often don't list the rim make and model.
Manufacturers have a funny habit of changing components like rims mid-year so the catalog might not be accurate.
Rims often suffer damage and are replaced, often with a non matching rim.

Brent

Any companies known to use relatively narrow rims for their frame, mountain, road, and track?

Why? Tires are usually the limiter when it comes to clearance.

I might prefer a narrow tire with a tight fit.

Campagnolo and Trek Matrix come to mind as far as being narrow.


Even Ksyrium SSC and Elite wheels were only 13mm inside width for most of their production years, as was the wide-looking MA2/MA40 rim!

Nisi Mixer rim was the narrowest inside width I've seen, possibly less than 12mm!

I just bought a pair of older Bontrager Race Lite wheels that had a refreshingly-wide 15mm inside width.

Are you looking for narrower rims? Should be able to get those cheap.

18.5mm outer width on those Nisi Mixers, wow! VeloBase.com - Component: Nisi Mixer

The OP's description matches the majority of 700C road rims manufactured since the mid-1970s. The only 700C rims that would be wider would be those designed for touring bicycles or hybrids. However, as noted in post #2, there are pitfalls.