Since it hasn't really been explained thoroughly after the .32ACP confusion, I feel obligated to mention a few things about the cartridges that the original guns fire.
Be careful not to buy a 7.65 luger, because that ammo is fairly hard to find and expensive.
Winchester_73 is talking about the 7.65mm Parabellum
cartridge, also known as the .30 Luger
or 7.65 Luger
. Although "30" implies that it's .30-caliber (0.308"), and "7.65" implies that it's .32-caliber (0.311"), it's actually neither; it roughly splits the difference at 0.309"-0.310" caliber. It's one of the few relatively common auto pistol cartridges that uses a bottleneck case, along with .357Sig and 7.62x25 Tokarev.
The 7.65 Parabellum round was the original cartridge used in the Luger pistol. However, the German military believed it was short on power, so DWM responded by straightening out the case walls, shortening the case slightly, and using a 9mm bullet. The German military accepted the larger-caliber round, and the rest, as they say, is history.
The original Luger pistols were NOT produced in .32ACP or .380ACP except for some exceedingly rare and valuable test variants, although one may occasionally hear someone incorrectly describe a 7.65mm example as a ".32"; see above.
Now to explain how this relates to the topic of "shooter" Lugers...
Despite the military's acceptance of the 9mm version, 7.65mm pistols continued to be produced, particularly once WWI ended and the Treaty of Versailles made it difficult for German industry to produce 9mm pistols. DWM quickly discovered that "new" 7.65mm Lugers could be built largely from reworked surplus wartime parts and then sold profitably on the commercial market. These factory-rebuilt guns are widely known as "1920 Commercials" and have relatively little collectible value due to large production numbers and an absence of military provenance.
IMHO a 1920 Commercial can also make a decent choice for a low-priced "shooter" IF one can deal with the ammo situation.
About the ammo... I'll have to disagree slightly with
7.65 Parabellum ammo IS available, and prices isn't outrageous IMHO, although it IS a good deal higher than 9mm. If you mail-order it in quantity, it can be had for around $22-$25 per 50rd box. Also, although the number of "shooter" Lugers is probably declining, the round will most likely remain in production for the foreseeable future because it is a moderately popular 9mm substitute in world markets where pistols in "military" calibers are prohibited (e.g. Italy).
One potential issue is that AFAIK there are no JHP 7.65 Para loads on the market, but then I'd argue that this pistol would be a categorically poor choice for SD/HD anyway. (I prefer that my defensive firearms be readily replaceable.)