Chief Ward (Jimmy Hunt) and Officer Kenney (Kenneth Kimmins) carry Colt Python revolvers as their sidearms. They're seen holstered in several scenes, but only taken out when the two confront David and Linda in the school.
M1911A1
The US Marines, particularly General G. Climet Wilson (James Karen), Sergeant Major Rinaldi (Eric Pierpoint) and Captain Curtis (Christopher Allport), use M1911A1 sidearms. They're also held by the two Martian-controlled NASA technicians in Wilson's office.
Rifles
M16 (SP1)
The M16 rifles used by the US Marines in the film are M16 (SP1) models with M16A1-style "birdcage" flash hiders.
Trivia: The U.S. Marine Corps supported the production with equipment and Marine Reservists acting as extras. Thus, the LAV-25s in this movie are actual LAV-25s. Along with Heartbreak Ridge, another movie which received USMC support, Invaders from Mars is one of the first films to feature the LAV-25.
Other
M47 Dragon
The Marine Squad Leader (Dale Dye) is seen using an M47 Dragon against the Martians. This is one of the earliest appearances of the weapon in a feature film or television series.
Mk 153 SMAW
An Mk 153 SMAW is used by a Marine to kill several Martians. The use of the SMAW in this film is notable, as the launcher had only just entered service with the U.S. Marine Corps in 1984, just two years before this film was released. This movie is likely the first-ever cinema appearance of the SMAW.
(Fake) M203 Grenade Launcher
Some of the Marines battling the Martians can be seen carrying M16 rifles fitted with M203 grenade launchers. These are the same fake M203 grenade launchers seen in various films made in the 1980s, such as Scarface, Heartbreak Ridge, Predator, etc.
M72 LAW
The M72 LAW is seen carried by some of the Marines in the film.