I'd scratch any modern S&W revolver (meaning anything with a number designation or anything not in .38 Special of .45 ACP). They may have been around, but it was at their inception, and an old .38 would have been far more likely to have been used, and a Colt more likely than that. S&W didn't start dominating the market until a while after the Cold War era began, but before that it was relatively balanced between S&W and Colt, if Colt wasn't the winner in the revolver market. If you want names, Colt Official Police and S&W M&P. According to a an archived High Road post, those were the standard issue of the FBI at the time.
I don't know how long any of the long guns you mentioned were issue, like the Ithaca 37, Winchester 1897 or BAR, or remained FBI issue past the prohibition era, the 1907 or the particular Thompson variant. Personally I'd be modest and leave it at two Thompsons, two period rifles of some sort, manually operated or autoloading, and then a shotgun of some sort, I'd say Winchester 1912, a bit more modern and prolific than the often seen 1897. The Ithaca 37 is more of a late 1950's - 1980's shotgun., and that's not including the specific run of the riot variants which may be dated later, though I'm going on what I've seen in various gun auctions and portrayal in media to be honest.
Just a word of advice too, when I pick firearms for something, I don't let something that was just introduced ever make the cut (for example, a Model 19 in 1957). Yes, it was apparently around at the time, but the transition from one gun to another usually takes some time, and generally, people like to fall back on what they know works, in the case of the 1950's, a Colt Government or a .38 revolver, and not a new flashy .357 Magnum. Today's fascination with more powerful calibers tend to lead people to forget that back in the day, it was what had worked and not what was the newest thing on the block that servicemen tended to appreciate.
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