Neuromancer defined cyberpunk. It is probably one of my favorite novels of all time. That does not mean it is good. It just means it is a keenly refined flavor that I have an acquired taste for. Connecticut, meanwhile, is a Bing Crosby musical from 1949 that I was required to watch far too many times.
Read the other two books in the Sprawl trilogy. They're pretty damn good and the only character they have in common is Molly. Islands in the Net by Bruce Sterling is a classic, albeit dated, but the whole genre is dated so that's okay. Mirrorshades is seminal. Hardwired isn't as good, but it sure is cyberpunk as fuck. Variation on a theme: The Difference Engine is Patient Zero of Steampunk and, in my opinion, the only book worth bothering with. I kinda feel like Paolo Bacigalupi picked up the torch where Gibson dropped it; Windup Girl is every bit as cyberpunk as The Sprawl, only the gadgets are biological, not cybernetic.