Original loading for the 1888 rifle utilised a 227-grain bullet at just short of 2100 ft/sec.
The 1904 loading, which is the original JS loading, shot a 154-grain flat-based, steel-jacketed bullet at 2881 ft/sec from the 29-inch tube. Your riffle should be safe for this loading.
The later loading with the 196-grain slug at 2700-and-odd was originally the ANTI-TANK loading for this cartridge. Pressures are 'WAY up there. Also nice high pressures with the SmK loading with the 178-grain steel-cored slug, which was cheaper to make than the lead-cored variety, especially when you are running short of lead.
Surplus ammo: that corrosive-primed Turkish stuff is the proper loading for your rifle. If you can find some of the Turk ammo, you put the powder charges and slugs into fresh primed empties, thus avoiding the salty residue that rusts your bore. This can be quite startlingly accurate.... if you can find some Turk ammo to play with.
The Portuguese M-937 loading is the JsS (anti-tank) loading and I would not pur it through a rifle that I like, although I HAVE done it and still have all my fingers and my rifle still has its chamber. The only really hateful thing about ignoring this ammo is that it is non-corrosive and it is just so DARNED accurate!
The Czech surplus loads that came in the 15-round boxes are the SmK loading: 178 grain slugs, pressures likely were high when the stuff was new.
For trying out your old rifle, use modern American factory loads. They have a 170-grain bullet and they will afford you the experience of shooting your antique. Once you have a supply of nice modern brass, you can start looking for some of those nice 154-grain .323" slugs and roll your own: double the fun and all for the same price!
BTW, these often had unit markings on the front barrel-band. Once ran into one marked to the First Infantry Regiment! Couldn't keep it, though!
Have fun!