1881 or 1882 Watham pocket watch

I have an inherited piece myself. The thing to do is to get some information to keep with it. I think they are worth protecting!
Here is how you start:

Rather than re-inventing the wheel, I'll simply direct you to this site:
http://www.antique-pocket-watch.com/waltham-pocket-watch-company.html
It gives a very nice history of the watch company to keep with the watch.

Then go to: http://oldwatch.com/identify/identify.html
to actually identify the important features of your watch.

Here is where you go to get the age of your watch:
http://barrygoldberg.net/waltham.htm
Your serial number is actually from about 1909-1910 (sorry, it's not an 1800's watch!)

Depending upon the exact details and style you should be insuring the watch for between $30 and $600 so it's worth identifying which it is! You didn't supply photos so I can't help you there. Check out the second website I gave you above.

Get as much history as you can from your relatives about the watch AND IT'S OWNER(S). WRITE it down and keep it with the watch too! Leave space on the paper for your name and how when you got it, AND for future generations to add to it. You and your future relatives will be fascinated if you do it right!

Now decide how you want to display it. In the 1800's and 1900's watches were a prized and expensive possession. When at home they were often placed into specially designed holders to sit on the mantel or a table to act as a room clock too. You can either pick up one of those antique holders (Warning! they are expensive!) or build one from wood and felt yourself, or check out other display stands and adapt them. I bought an antique mantle clock stand that hung the clock from an archway in it's design. The clock was missing from the piece but I could feed my pocket watch chain through the hole, so that the watch hung high and the decorative fob hung below. A simple tooth pick holds the loop from falling back through the hole of the ceramic piece. Looks great! My documentation sits in a small decorative box beside it. But a framed sheet would look good too. You can buy frames at specialty shops (I use Micheal's myself) that have a deep recess (usually to frame objects such as baby shoes etc.) so you can actually keep all your paperwork together and only display the one you want on top!

Hope this gives you some ideas!