A 32 Charter Undercoverette from the 1970's would have been made for 32 S&W Long. That cartridge is also sometimes called .32 Long, because nobody has made revolvers for any other 32 Long cartridge since about 1920. Also, some gun companies do not like marking their guns with "S&W". For that reason Colt used to call this same round "32 Colt New Police", and some ammo companies used to sell it under that name, but that died out 50 to 60 years ago, I think. That round is NOT the same as 32 Long Colt, which was dimensionally different, and was one of those cartridges nobody made guns for after 1920.
At the time this gun was made, 32 H&R Magnum did not exist, and nobody was making snub-nose revolvers for .32-20 Winchester. You can use the shorter just plain "32 S&W" in it, but I don't know why you'd want to; it is hard to find, will not shoot to the same point of aim, and is too weak for just about any purpose at all (besides paper punching from certain highly specialized automatic target pistols).
There are two main bullet styles available for 32 S&W Long: round nose lead (RNL) and wadcutters WC). Wadcutters look almost like blanks, but they have a soup-can shaped bullet loaded way down in the case. Target shooters like wadcutters because they cut perfect circles in a paper target and make scoring easy. (The circular pieces of paper they punch out look like miniature old time paper shotgun wads, which is where the name comes from.) They are about equally useful for self-defense; people hope the RNL has more penetration and that the wadcutter has more shock on impact, but that is a subject of bitter debate. Round nosed bullets are significantly easier to load or reload the gun with in a hurry, because they are pointy instead of blunt.
An Italian company named Fiocchi makes a round-nosed full metal jacket bullet (FMJ) load in 32 S&W Long. The FMJ bullet does not make much difference, but in my experience, the Fiocchi ammo was loaded a little hotter than American 32 Long loads. I don't know if it still is. Fiocchi sells a lot of ammo in the US, but it can be hard to find at stores, as opposed to gun shows (also in my experience). It is sometimes cheaper than US ammo as well.
What you really want for self-defense, according to today's thinking, are bullets that expand on impact, most commonly "hollow point" bullets (HP). But I don't know if any major ammo manufacturer loads those in 32 Long. There is a small company called "Buffalo Bore" that might; even if they don't, if they make 32 Long in any form, they will load it hot. That is their specialty.
Sorry I have rambled on so long. I hope some of it is helpful. 32 Long is one of my favorite cartridges, and it is a pretty good choice for someone who does not shoot much and could easily develop a bad flinch with a pistol that has much recoil. You might want to look into getting oversize rubber grips for the gun anyway; the Pachmayr company makes a great variety of them. You can search for them on Ebay.
PS - 32 Automatic would sort of fit, and might fire most of the time, but it is undersized, overpressured, and may give bad accuracy. Don't try it, is my advice.
