I would say "handsome" falls more under genetically appealing, typically.
However, with the phrase, "A handsome sum of money", handsome would mean large, generous or copious . (quasi-formal)
I'd say, "nice car" or "beautiful car" and "pretty flowers" or "beautiful flowers"
It also (almost always) depends on the formality and type of the people you are speaking to.
"Gorgeous flowers" would be something a female would say, but most probably not a male. It would sound effeminate if a male did.