How common is stomach cancer in the U.S., and does it mostly affect certain types of people, such as meat-eaters?

Not very common. Stomach or gastric cancers have decreased in the US since the 1940's. There are some stomach cancers however associated with H. pylori stomach infections. Smoked foods, excess alcohol intake, and cigarette smoking may be associated with stomach cancer. It is more common in other countries than the US.
Not common. There are about 20, 000 new cases of stomach cancer each year. It is more common in the elderly, those with gastritis or ulcers caused by h. Pylori, those who eat very few vegetables or fruits and eat alot of salted, smoked or preserved foods, drink too much alcohol and smoke. So your question about meat eaters is true, especially if the meats are the smoked or preserved variety.