Travis Bickle (Robert De Niro) purchases four handguns from "Easy Andy" (Steven Prince), the illegal gun salesman. The first of which is a Smith & Wesson Model 29 with an 8 3/8" barrel, the longest factory barrel made for the S&W Model 29 during this time period. The other two stock barrel lengths at the time were the 4" barrel and the 6.5" barrel. Travis apparently gets the idea of owning a .44 Magnum from one of his passengers (played by director Martin Scorsese) who claims he will use it to murder his cheating wife. Travis's Model 29 is seen often throughout the film, carried in a large shoulder holster he purchased from "Easy Andy" for $40, in addition to paying $350 for the revolver itself.
Smith & Wesson Model 36
Travis Bickle (Robert De Niro) also purchases a nickel Smith & Wesson Model 36 with a square butt, mother-of-pearl grips, and a flared flat cylinder release hatch (dating it from the late 50s to early 60s) after "Easy Andy" (Steven Prince) suggests it as a more practical weapon. Travis purchases it from him for $250. A mobster in the whorehouse during the final shootout has a blued Model 36, which Travis takes from him and uses.
In a continuity error, the S&W Model 36 becomes a nickel S&W Model 10 Snubnose when Travis fires it at the range (see below).
Smith & Wesson Escort
Travis Bickle (Robert De Niro) also buys a Smith & Wesson Escort from "Easy Andy" (Steven Prince), who incorrectly refers to it as a "Colt .25" and sells it to him for $125. Travis attaches the S&W Escort to a drawer slide, mounting it on his forearm and later using it during the final shootout. In a continuity error, this is seen as a Sterling Arms pistol when Travis is firing it at the range.
Astra Constable
Travis Bickle (Robert De Niro) buys an Astra Constable for $150 from "Easy Andy" (Steven Prince), who not only mistakenly refers to it as a ".380 Walther", but also claims that "during World War II, they used this gun to replace the P38. Just gave it out to officers" and claims it can hold eight rounds in the "clip" (meaning magazine). This is the only handgun Travis buys that he doesn't keep in any sort of holster, choosing instead to tuck it in the waistband of the small of his back. He hands it to the grocery store owner (Victor Argo) after killing the robber with it. In a continuity error, this is seen as a Walther PPK (most likely the actual weapon Andy was referring to) when Travis is firing it at the range.
M1911A1
One of the weapons in "Easy Andy"'s case of handguns is a M1911A1.
Luger P08
Another of the weapons "Easy Andy" offers to sell is a Luger P08.
Walther P38
In "Easy Andy"'s second case of handguns, a Walther P38 is seen.
Colt Official Police
Four Colt revolvers, at least two of them being Colt Official Polices, are offered by "Easy Andy" in his second case of handguns.
When Travis Bickle (Robert De Niro) fires his handguns at the shooting range, his S&W Escort is now a Sterling Arms pistol.
Walther PPK
When Travis Bickle (Robert De Niro) fires his handguns at the shooting range, his Astra Constable is now a Walther PPK.
Colt Detective Special
When Travis Bickle (Robert De Niro) fires his handguns at the shooting range, his nickel S&W Model 36 is now an early-model nickel Colt Detective Special.
Smith & Wesson revolver
A robber (Nat Grant) attempts to rob a grocery store with a nickel plated S&W five-shot revolver, but is stopped by Travis.
Smith & Wesson Model 10
Iris's pimp Matthew, a.k.a. "Sport" (Harvey Keitel) fires a nickel Smith & Wesson Model 10 at Travis. Some NYPD officers also carry standard Model 10s.