Rico (Lee Marvin) carries two handguns in the movie, the first one is a Colt M1911, which he carries in a military-style holster (he also carries a double magazine pouch.)
This Official Police is an anachronism, as production did not begin until 1927, and the Mexican Revolution is generally considered to have ended in 1920. However, the very similar Army Special was in production at the time, and could have been carried at the time the picture is set.
Colt New Service
Hans Ehrengard (Robert Ryan), Jesus Raza (Jack Palance), and his "lieutenant" Chiquita (Marie Gomez) use Colt New Service revolvers throughout the film.
The Winchester Model 1897 shotgun is the main gun used by Henry "Rico" Fardan (Lee Marvin) throughout the movie. Later in the film Bill Dolworth (Burt Lancaster) takes it and uses it to great effect against Raza and his men.
Rifles
Winchester Model 1892
The Winchester Model 1892 rifle is the most common rifle used by the "Professionals" in the film, being utilized by Hans Ehrengard (Robert Ryan), Jake Sharp (Woody Strode), and Bill Dolworth (Burt Lancaster), the latter using one to good effect against Raza and his men near the end of the film.
M1903 Springfield
The most common bolt action rifle in the film is the Springfield M1903, used mostly by Raza's men. Earlier on, the "Professionals" acquire some M1903s from some bandits. Bill Dolworth (Burt Lancaster) takes a Springfield M1903 as he holds off Raza's remaining forces as the group make for the US-Mexican border.
Springfield 1873 Trapdoor Carbine
The Mexican Army Soldiers aboard the train are mostly equipped with the Springfield 1873 "Trapdoor" Carbine, a stark contrast as the Mexican Army's main rifle during the Mexican Revolution were Spanish Mausers.
M1 Garand
A (Highly Anacronistic) M1 Garand is seen in one of the saddle scabbards on one of Raza's men's horses.
Machine Guns
Browning M1917
The Browning M1917 machine gun is first seen being demonstrated by Rico to the US Army at the beginning of the film. It's later seen used by the Mexican army when Raza's men ambush the train.
Vickers Machine Gun
In a continuity error, the Browning M1917 used by the Mexican soldiers aboard the train during the ambush by Raza's men turns into a Vickers Machine Gun as Raza (Jack Palance) tramples over the machine gun crew with his horse, knocking the Vickers off the flatcar.
Lewis gun
Another machine gun used by the Mexican army on the train is a Lewis Gun, which is captured by Raza's men once they take the train. Henry "Rico" Fardan (Lee Marvin) Later commandeers it during the ambush at Raza's hideout. He later uses it to great effect against Raza's men when the "Professionals" escape with Maria Grant (Claudia Cardinale) aboard the train previously taken by Raza and his men. Interestingly, this a US-issued Model 1917 Lewis gun, identified with it's cocking handle placed on the left side of the receiver, and chambered in .30-06 for use by the US Marines during World War I.