I can't remember much. When I got myself IV, all I did was have fun and didn't really think about anything, didn't compare it to other games or anything. I was suprised by LCHC at first, while I found the music to be top notch, it took some time getting used to the vocals. The only clear memories I have are from my multiplayer days:
I had the game since around 2010, and spent about a year or so messing around in Singleplayer. I had a friend that I played SAMP a lot with, and he always told me to get on IV multiplayer. I eventually figured out how to set up the internet on my PS3, and I was invited by the same friend to a Multiplayer race, Drag Kings with Muscle Cars. Being my first race, I won very easily against my friend and a couple of other random players. Overall I was a noob, switching between Auto-aim and Free-aim matches until finally deciding for Free-aim, but my primary game mode was Race. Oh how enjoyable they were. There has never been a better feeling than beating other racers with slower or more difficult to drive vehicles, laughing that they lost to a SuperGT or a Zombie chopper. The driving mechanics were so good I prefered IV Multiplayer Racing over any other game. They just felt right.
Soon I developed my own set of crazy codes that I would follow for the next few months, involving things like 'Driveby is not fair, only shoot on foot Comets are for pussy fags in Race, I only use with Pistols because everyone else sucks' (well the random players you find in lobbies did suck hard, involving high ranking players who couldn't kill without RPGs or corner shooting glitches) etc...
In some way I turned into a crazy ass hipster, until I matured and started to get along with the GTAF community and their gangs. They were a great group of skilled and friendly players (ajbns, madmonk, illadope, andyganteks, highwayreaper, tox1c, etc...) with whom I would participate in Events.
I have some very pleasant memories of things I did playing Mafiya Work, I would get a police car and instead of doing objectives, I would make it harder for everyone else to do them. I was sort of a Vigilante player while playing that game mode. It was very fun to do, but at the same time I felt a bit bad for annoying other players by camping the objective or similar...
There was always a struggle for me to find like-minded players, people who would instead of playing the 'popular' and 'sh*tty' match settings, only the fasters cars, only on Sunny weather, would rather play something different and unique every time. I only found a few, one of them being Dealer_Of_Spades, who would become my best GTA friend and partner, who I would always play any gamemode with, racing with Muscle Cars or Choppers on Wet Roads for a more challenging, fun experience.
Onto the Free Mode aspect, playing with the police off, traffic off, beating up pedestrians with Fists, Baseball Bats or Knifes, continuously taunting them with funny lines and counter-attacking them was one of the things I really loved doing. Shame that these features weren't even in the Singleplayer mode, who wouldn't like a cheat to turn off the police, traffic, or the ability to taunt pedestrians (especially when the Taunt button didn't do anything in SP while on foot)
Well that's about as many memories I can think of right now.