Since I'm really passionate about the band, Rush, I figured I'd give you my three favourites from each album (listed from third favourite to favourite) and say, go check 'em out because they're amazing, and you'll wonder, "How can only three guys do this??"
Rush (1974): In the Mood, Finding My Way, Working Man
Fly By Night (1975): By Tor and the Snow Dog, Rivendell, Anthem
Caress of Steel (1975): Bastille Day, The Fountain of Lamneth, The Necromancer
2112 (1976): A Passage to Bangkok, Tears, 2112
A Farewell to Kings (1977): Closer to the Heart, Xanadu, Cygnus X-1
Hemispheres (1978): The Trees, Hemispheres, La Villa Strangiato
Permanent Waves (1980): Jacob’s Ladder, Freewill, The Spirit of Radio
Moving Pictures (1981): YYZ, Vital Signs, Witch Hunt
Signals (1982): Subdivisions, Losing It, The Weapon
Grace Under Pressure (1984): Afterimage, Red Sector A, Distant Early Warning
Power Windows (1985): The Big Money, Grand Designs, Mystic Rhythms
Hold Your Fire (1987): Force Ten, Lock and Key, Prime Mover
Presto (1989): Red Tide, Available Light, The Pass
Roll the Bones (1991): Dreamline, Roll the Bones, Bravado
Counterparts (1993): Cold Fire, The Speed of Love, Nobody’s Hero
Test For Echo (1996): Carve Away the Stone, Resist, Half the World
Vapor Trails (2002): Earthshine, Peaceable Kingdom, Ghost Rider
Snakes and Arrows (2007): Far Cry, Hope, The Main Monkey Business
Clockwork Angels (2012): The Anarchist, Halo Effect, The Garden
If you do decide to listen to any of these, listen to the lyrics. They touch on philosophy, science, fantasy and history. Pay attention to the year the album was released, as you'll hear a change in the overall sound. They also have some great guitar solos, drum solos and keyboard solos within these songs. Enjoy!
PS. No, they did not change singers. He just really learned how to sing instead of screech. The did however, change drummers between 1974 and 1975.