That's a good question. I would say .357 magnum just because I think it would give you the most power possible out of the short barrel, especially using the "short barrel" specific ammunition. I don't think they make a .44 magnum version. The 9mm is really only a viable self defense caliber when it's pushed fast. That's not possible in a barrel this short. The other end of the spectrum is the tried and true "big slow bullet" method where something like a .45 Colt or .45 acp pushed as fast as you could manage in such a short barrel. Of course you have to meet the expansion limit of whatever bullet too which is difficult with barrels this short. I'd love to see a bunch of different calibers tested in ballistics gel for expansion out the Bond Arms derringer just to see what expansion, if any, is possible.
Might be the perfect platform for fluted lightweight bullets like the Inceptor ARX. The light bullets will go much faster than standard versions out of the Bond Arms and the fluted design means no hollowpoints to expand. That would make a fascinating video.
This is mine, it's the Bond Arms Bond Girl Mini .357 magnum. I call it the "Noisy Cricket" (movie reference). It definitely has a noticeable recoil with normal .357 magnum ammo but it's not terrible. You wouldn't want to shoot a box full though (or even a half a box) lol. For me, my hand has had enough after about 8 or 10 rounds.
We had it at an indoor range one day and there was this small group of big guys from the local university there. They were taking turns shooting what I think was a .44 magnum revolver one of them had brought along. They started watching my sister and I shooting the Noisy Cricket so I asked if they wanted to shoot it and they said "no way, not a chance" lol. The little derringer just looks painful when you see it being fired but it just looks worse than it is. It definitely stings your hand but it's not terrible. With hotter .357 mag ammo I agree it would not be fun at all.