Revisiting this awesome game after 15 years (got my old CDs to work after some hassle). \o/

Decided to get 100% of the game and that means getting everything unlocked and finished, which in return means I have to (gladly) replay the Story to unlock most cars and play Free Ride Extreme missions to unlock 19 special cars (I know there is a quick way of doing this but would still prefer to actually pass missions are earn the cars).

So, my concern is about the Story unlocks. I don't remember how this used to work and my Google Fu didn't provide any satisfying results hence this thread.

Is there a certain way I should be doing things to make sure I don't miss any of the cars?
How does the game save car unlocks, do I have to do something in a particular way or is it enough just to find a car, enter it and the game will "remember it"?
Should I reach some point in Story and then are all cars unlocked and I could relatively easily "get them all" by wandering around or are different cars available in different part of Story or different parts of city?

If your question is "did story mode have some misselable unlocks?" - yes it have. There is mission one of first where Fire Trucks spawned and they not locked. Most else cars should be unlocked during main and optional missions.
Should be stealed and parked at Story mode garage.

Mission about stealing case docs from prosecutor home (mansion) - keep it stealth way until prosecutor driver park car in garage. At some point you can steal it (and maybe there is point where it cannot be stealed- garage locked or some like that). Closing garage happen earlier if you rush to exit when game tell you you not need stealth anymore.

Find Mafia Fandom Wiki and check cars lists. There is more specific conditions. In Story, Free Ride.
Some fan sites, but probably they dead. Fandon is first place.

Steam game hub Guides.
Russian fan site is still alive
http://gta.ag.ru/mafia
It have link to differ types of secrets (easter eggs also) and it uncomplete
http://gta.ag.ru/mafia/secrets
and its russian. But it have screens.

Red 60' bolt thrower can be unlocked during any mode and in Story at any mission since you start to work for mafia. Park and save one at garage save-load and bring another one.