New (to me) 1982 Trek 613
 

After a couple weeks combing Craigslist for an old road bike my size, last night I picked up an all-original (right down to the water bottle!) 1982 Trek 613. Looking up the serial number, they're actually calling it a 610, which I believe specifies just the frameset. But all the components match the specs for a 613. Everything shows very little wear and it basically looks like it's sat in a garage for 25 years unused. Just the brake hoods have rotted and will take some effort to scrape off and replace. Any sources for (cheap) brake hoods for these Dia-compe levers?

Ta da!

http://www.velo-orange.com/cacrbrnobrle.html

Beautiful! Ordering a pair now. Other than that and adding a rear rack, I think I'll leave the bike as is. I plan to use this for light commuting and don't want it to look TOO nice (i.e. valuable). It's a good rider in its present state. I just need to adjust to friction downtube shifters!

I think I have a 613. I know I have a really pretty Trek of that vintage and it seems to match the 613 description in the catalogue but I don't know how to tell for sure.
I really need to take some pictures but I've been a little pressed for time lately.

I think you nailed it. Its the 610 family. The build components dial it in, use the catalogs (which I think you did) to narrow it down. I had the same issue with a 412 I had. Showed up as a 410 in the serial number table.

sailorbenjamin, you can find the serial number located on the bottom bracket and then go here:

http://www.vintage-trek.com/SerialNumbers.htm

to find out the correct model and year of your Trek.