People budget to buy engagement rings at 3 times a month's (not year's) salary and wedding rings at much cheaper cost (could be dirt cheap at 20,000 - 50,000 yen or slightly higher at 100,000 yen, but these are definitely cheaper than even ONE month's salary). Source: my Japanese wife

O-toshi-dama is a mix of affection and duty. My kid gets the money from some but not all of his aunts and uncles (and certainly from his grandparents).

Omiyage (like returning from a vacation or business trip) is more a thing of duty, IMO.