I'd recommend Uncut Radio mod (over 60 songs from 40s and 50s), but it's currently hidden. Both Mafia and Mafia 2 have a special place among my favourite games.
I’d say it’s definitely worth it, especially on Hard.
Word of warning: it will frustrate you. The Observatory on Hard is grueling. But it’s worth it in the end, and tbh it’s the way it was meant to be played imo.
They never really explored the family aspect of the mob and relations between other families enough for my taste, I'd enjoy seeing more of that instead of III's new up and coming leader snooze-fest.