I was just the right demographic and everything for Halo. Had an Xbox. Had the game. Had 4 brothers to couch co-op with. Was a weird backwards military-obsessed family.

Played it a bunch. A BUNCH. But while I enjoyed it, it didn't really leave any kind of impression. I thought its story was shallow and its characters unremarkable caricatures even at age 13. Years later when I saw people going on about how DEEP its world-building was and how BADASS Master Chief was and how ICONIC the game was I was just kinda...nonplussed? Whole game was just mediocre to me. I mean, that's not to say I didn't like it or whatever, but it wasn't groundbreaking for me the way it was for (apparently) many others.

Make of that what you wish!

I didn't really grow up with it as others but I think I got into it enough that I can try and answer you.

So, the first one was the first game to figure out FPS in consoles that really took off (most likely the first one to do it, but you never know, I might stand corrected). Some people will point out to Goldeneye on the N64 but I really doubt any game was playable on that three pronged controller let alone an FPS.
I remember they did some trickery with the aim to compensate for the stick as an input method, and they also set up the two weapon limit which is now a staple.

Another aspect is the multiplayer, which was great both as a couch split-screen and online; you also had the forge so you could get creative with it.
You know, if you're having fun with your friends that's all it takes to fondly remember everything that came with it, and a videogame can play that role, whether it's actually good or bad.

As for the story, I'll admit the mainline story was just fine for me, not lacking for the kind of game that it is, but halo reach on the other hand really struck a chord with me.