.38 long colt.
I bought a colt .38 in the 50's. (made in 1901)
It has straight thru chambers, well only a slight taper anyway.
And the barrel has a .357 bore with .364 grooves.
Early models had something like .380 chambers and .380 grooves in the barrel. The bullets were heeled, like a .22 long rifle. The final design was the .38 special with about a .380 case and a .357 bullet. Mine was an in between design, why I don't know. Nor do I know what should be shot in it.
I use to shoot .38 specials with lead bullets, but got a lot of flyers. Perhaps 148 grain hollow base wad cutters would expand enough to fill the grooves and with .357 brass could come close to the end of the cylinder.
I have seen .38 long colt ammo, but without a description of what chambers or barrel groove diameters are expected.
So it seems to me, the first thing to do, is to find out what chambers and throats are in the cylinder, then what bore and grove diameter are in the barrel.