I don't think this topic have been done before, I might be wrong.
I'm curious to know, how were you introduced to New Order's music? Might be evident for some people that will say "Blue Monday was playing at the radio", but for some other, it's a friend or family member playing it and that's the way you knew who New Order were, and not some random band.
As for myself, of couse I knew Blue Monday, Bizarre Love Triangle, but the first time I bought a record for a New Order song was the Bright Lights Big City soundtrack, for True Faith. Although I knew "New Order", I was introduced REALLY to the band by a mixed tape done by Sebastien, the co-webmaster of this website...
I was there when he bought the first Electronic album too, so I became a fan of Electronic around the same moment... the mixed tape contained a lot of different songs (we used to put remixes on those tapes back then), it took me a while to be able to stand In A Lonely Place for instance, and a few other songs, but I got attracted to Round & Round quite fastly... then I learned that New Order was behind Blue Monday and BLT, which I didn't knew before.
First album I got is Substance, took me a while to like the first songs of the album, but I managed to love them all!
Then it goes on that 10 years later I started a website
Oh well... ;)