Jonathan Byers (Charlie Heaton) takes his father's Smith & Wesson Model 10 when he and Nancy Wheeler (Natalia Dyer) set out to find the monster in Myrkwood in "Chapter Five: The Flea and the Acrobat" (S01E05). She later uses it to fight the Demogorgon in "Chapter Eight: The Upside Down" (S01E08). It also appears to be the weapon used to fake Benny's suicide in "Chapter Two: The Weirdo on Maple Street" (S01E02)
The Beretta 92FS appears to be the sidearm carried by the Military Police personnel at Hawkins National Laboratory. While the Beretta 92FS (probably standing in for the Beretta M9) is period correct for Season 1's setting in 1983, the use of the pistol is anachronistic since the M9 pistol was not adopted by the U.S. military until 1985 (and did not enter service widely until 1990). It would be more accurate for the MP's to be issued with the Colt M1911A1 like the government agents. The majority of these pistols in the series appear to be replicas.
Error creating thumbnail: File missingBeretta 92FS - 9x19mmError creating thumbnail: File missingA Military Police officer holds his Beretta 92FS and a government agent holds his Colt M1911A1 on Chief Jim Hopper in "Chapter Five: The Flea and the Acrobat" (S01E05). Note how these appear to be either dummy or airsoft replicas.
Colt M1911A1
The Colt M1911A1 is carried by government agents including Connie Frazier (Catherine Dyer). Chief Jim Hopper (David Harbour) is issued one when he and Joyce venture into the Upside Down in "Chapter Eight: The Upside Down" (S01E08)
Heckler & Koch MP5Ks with Navy trigger packs, sometimes fitted with a flashlight, are used by government agents and MPs throughout the series. Jim Hopper uses one in "Chapter Eight: The Upside Down" (S01E06).
Heckler & Koch MP5Ks with PDW stocks attached are also used by agents. Since the show takes place in 1983, this is considered anachronistic since the MP5K-PDW variant was not developed until 1991. Some of the stocks actually look to be UMP-style stocks, making them even more anachronistic.
The Double Barreled Over/Under Shotgun appears on display to a mannequin in the hunting store Nancy Wheeler (Natalia Dyer) and Jonathan Byers (Charlie Heaton) go to buy supplies and traps from in "Chapter Five: The Flea and the Acrobat" (S01E05).