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.
U.S. Marine Corps LAV-25s in the film are fitted with the M242 Bushmaster chaingun. Trivia: The U.S. Marine Corps supported the production with Marine Reservists acting as extras and equipment, and 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 Mod 0 SMAW
AMk 153 Mod 0 SMAW also appears to be one of the launchers used by the Marines.
M203 Grenade Launcher
Some of the Marines battling the Martians can be seen carrying M16A1 rifles fitted with M203 grenade launchers.
M72 LAW
The M72 LAW is seen carried by some of the Marines in the film.