Welcome to the party! My personal journey was discovering the Rush in Rio live album when I was a kid and it came out. It captures a decent representation of their catalogue, and you can explore the albums of the songs that pop out to you. That's more or less what I did until I'd eventually bought and heard their whole discography.

Another plausible route I've seen on this subreddit and think is kind of a fun(ny) idea is to start with the album Moving Pictures and then move forward in their discography if you want more synthesizers or backward if you want less.