'Vacker' is a lot more used about women than about men. People that are 60 years or older would typically say 'en vacker kvinna' and 'en stilig man/karl/herre'. I think 'stilig' is the most fitting translation to 'handsome' but it sounds quite old fashioned nowadays.
Younger people more tend to say 'en snygg tjej' or 'en snygg kille', at least about people of the same age.
'He/she is really good looking' would translate as 'Han/hon ser väldigt bra ut'.
It depends on what is beautiful. It would be a bit weird to say 'ett fint barn', unless (maybe) talking about 'fina familjer' (aristocracy, upperclass). A dress could be both 'fin' or 'vacker'. But there is a difference anyhow. Beautiful = Vacker, but 'fin' is more like 'nice'. So it depends.