Weibel

Seeing you want a "nitro express" round in a standard 98 actioned rifle which doesn't cost too much.

Some ideas I would consider myself. And keeping with your stated theme. Aiming at cartridges designed for a bolt action. I don't know what animal size or calibres you are thinking about but here is a few to consider.

The .318 Westley Richards. .330 calibre on a case not much different from a .30-06 sized case. Indeed .30-06 brass is said to be able to be used if original .318 WR headstamped and sized brass is not available. The original classic cartridge behind all the later pretenders such as the .338 Win Mag, .338/06 etc. A .30-06 could be converted with a new barrel and minimal work on the feeding, magazine. Others could comment on that. Projectiles from 180 grs to 250 grs. The 250 gr FMJs and RNSP were a standard in their day.

.404 Jeffery. .423 calibre. Originally loaded with a 400 gr projectile at about 2,150 fps, now loadable up to say about 2,400 fps. Able to be chambered in a standard M98 action.

.500 Jeffery. Again able to be chambered in a standard length action. A true powerhouse.

.375 H&H Mag. The easiest NE round to obtain.

I think all of the above do have NE designations as well ???

Most of the rounds we know as Nitro Express are rimmed, slim cartridges designed for the new fangled cordite sticks, as compared to black powder. Some of these were chambered into bolt actions but generally not the best idea and more gunsmithing required.

Some others to consider include various 9.5mm's/.375's.

All depends on what you are aiming for.