The breastplate, chainmail and helmets of the Arnorians very closely resemble these late-medieval Italians (from Perry miniatures):
The shields and spears are mostly copied from Gondor I guess, to show their relation. Greaves aren't very specific.
The rangers are just those of Gondor, which aren't very historical in any way, just your typical woodland dwelling scout.
Pretty much no information from the books is available concerning Arnor's armies, be it tactics, units, equipment or anything else. The later rangers evidentially used bows, swords and spears and worn some armour (helmets at least), based on the Grey Company. Those can hardly be described as an army however (most closely resembling Robin Hood's outlaws), and may not resemble the original Arnorians very much (seeing how over a thousand years pass between the Fall of Fornost and the Grey Company). In short, they can resemble anything you want, as there isn't much to go on in the actual sources.