First let me congratulate you on your wonderful find. It is unusual to find a five piece of anything in early silver. It is likely what is known as "Coin silver" and not sterling. This does not detract from it's value or importance. To clean the silver will require patience and quality non abrasive silver polish, Hagerty is one of the brands. Do not use a dip! It may take several tries to remove most of the tarnish. Try not to remove the dark areas in recesses of design.
I would love to see images of the pieces and the marks if possible. Your $10 purchase is probably worth several times that.
I must retract my quick assessment of your teaset. I am not certain that what you acquired is coin silver or silverplate. This firm made many plated items. It is certainly worth much more than the ten dollars you paid. If you can send me an image of the set and marks I might be able to help further.
Since I came here asking questions, I thought I'd try to contribute, as well. In your description of the tea set you bought (what a lucky find!), you said it consisted of: "large teapot, smaller teapot, cream, sugar and some kind of urn." The large tea pot is probably a coffee pot....they are taller and narrower, tea pots are lower and wider. The urn is likely a waste bowl. When they steeped tea leaves in the tea pot, they poured it out into the cup through a silver strainer....and dumped the escaping leaves into the waste bowl. It was also used to pour out cooled tea when you got a fresh cup. I can't remember if you rinse out a silver teapot before making the tea; I know you do a china one. Some tea sets also included a hot water kettle, on a stand over a candle to keep the water hot. You learn stuff like this growing up in the South....or at least you used to. :-)