For physics/handling I can pick up immediately and don't mind how the content was, but still made an impact in personality/as much as was there, GT3.
For the extra content GT 2001/2002 Concept. For other content or ideas GT4, physics is ok not my thing.
I prefer GT4 Prologue's license tests/driving missions then I do GT4 retail's actually. Even the coffee breaks are better in GT4 Prologue I find.
Online is fair. Tourist Trophy could do with more but is still a good game for what it offered of progression and the bikes. It stands out on it's own even compared to Riding Spirits, MotoGP, Ride or other bike games.
To me it's tied between GT3, GT2001/2 Concept or GT4/TT.
GT3 I guess. It has enough besides it's limitations that I enjoy it more. But it is a really hard pick for the additions or unique content GT Concept, GT4 Prologue, Tourist Troophy and GT4 have.
GT4 is a good game but eh, it to me is just GT2 with more to it. Like sure it stands out and yes GT3 is GT1 and 2 combined with whatever it could for PS2.
Like GT4 has driving missions and a enough variety in it's event types and more cars sure, and online for those that want the multiplayer experience which I don't care about.
But it's also got GT2 style manufacturer events and to me many are strict tracks I don't like so the randomiser in GT2 is way more fun to do however I want on tracks I want even if have to recycle a lot.
So while they borrow from past games and expand on them or make them their own I also prefer some of the older entries ideas as well.
But they are all so good as well these games of that era it's herd to pick one too, because they offer so much good stuff in progression, event requirements and variety of cars. I don't just go for the cars/licensed tracks or music as to me that's fine but the core gameplay and menu use is why I like the games not because favourite cars/tracks are there. You can give me no license music, track or cars and be original and I'd still play a racing game it's just many of the ones these days are so focused on what they are or don't even offer the same care of modes as others of PS2 era anymore.
GT 2000 is an ok demo but it has to have more to it, it doesn't so yeah no, meme status doesn't count to me. Impressive demo sure, but nothing more than that.