RE: appropriate cartridges for short barrels?
Short barreled (carbines) are sweet handling guns anywhere the cover is heavy or there is some demand for fast handling.....but don't think that short barrels mean short cartridges. A short barreled .270, .30-06, or even .35 Whelen is a superb choice for the thick cover hunting.
While the .260 7MM-08 or even .308 are great cartridges, there's nothing about them that excell in short barrels over their longer counterparts.