I will tell my story in phases, a la TheAccountant.
#1 - Spring of 1981 - I was 11 years old, not really hip to any bands or music beyond pop. Songs I knew at the time were Whip It, Cars, and Pop Muzik, the later I had on 45. I had received Billy Joel's album Glass Houses on my 11th birthday (May of 1980) and I liked it quite a bit. Fast forward to March or maybe early April of 1981 and I here people talking about a band named Rush and a new song called Tom Sawyer. It's just three people, and it's so good. One Saturday I'm watching tv (not MTV, just regular tv, so I don't know how this happened) and the video for Tom Sawyer comes on. I thought to myself, "This is the band and song I've been hearing about." So I watched it, and I didn't like it. It sounded weird, they didn't look like rock stars, the singer looked like a witch, and what was with that shrieking? (On a side note, late in 1981, or perhaps early in 1982, I probably saw King Crimson perform on the show Fridays. I watched it religiously, and they definitely appeared, but I probably thought it was wacked out weird shit.)
#2 - Here's where my timeline is a little bit foggy. Sometime in the fall of 1984 , I was part of the Columbia House record thing. The album of the month that they sent out was Moving Pictures. I kept meaning to send it back, but I missed the dead line and had to keep it. I had been getting into Yes quite heavily, so Moving Pictures just went down in the stack of albums my parents had, along with the few I possessed. In late 1984, was talking to a neighbor friend about wanting to add a band to my listening, feeling that listening to only Yes, I was going to burn out. He suggested Rush and loaned me All The World's A Stage. They have the best drummer and the best bass player, he said (we'll see about that!) After listening to it, I was sold on Neil, still thought Chris Squire was better than Geddy, but not by much, and the guitarist was criminally underrated. Rush was on my radar.
#3 - February 1985 - We'd had a pretty good snow storm that had shut down the schools for a few days. We had cleared off our driveway, and the snow plows had come through, and my parents and I went to the grocery store. While they were shopping, I walked next door to the record store, which surprisingly was open. They didn't have any Yes that I didn't already have, so I looked in the Rush bin. I can't remember all of what they had, but they did have Grace Under Pressure. I knew that was the most current album, and I liked what I'd heard on the radio (Distant Early Warning and The Body Electric) so I bought it and listened to it as soon as I got home. I can still remember hearing the last three songs on side two for the first time. I don't remember how many times I listened to Between The Wheels that night.
#4 - Spring of 1985 - I was listening to Moving Pictures and Grace Under Pressure, but I needed something more. Since I liked Yes, and loved their longer pieces, I knew Rush had the album 2112, and that side one was the song 2112. So I bought it one day after work, and that was that. I didn't need there to be any good songs on side two (but there were) I just needed 2112, over and over again.