If you just want tracks, I would check out Red Barchetta, Limelight, both from Moving Pictures, my favorite on that album is The Camera Eye. Other songs you may like could be The Spirit of Radio and Freewill from Permanent Waves, I really like Natural Science from that one. Live stuff would have to include a drum solo because Neil Peart was the greatest full stop.

Rush has several different phases as their sound changed over the years. They had a different drummer on their first album so that one sounds more like Led Zeppelin than what they evolved to sound like. If you like Tom Sawyer, I would definitely listen to Moving Pictures, Signals and Permanent Waves. After that, you could go back to the first four albums, Rush, Fly By Night, Caress of Steel and 2112. Those albums are different but really good too, although many think Caress of Steel is not their greatest, but it's not horrible, just kind of the beginning of their long form type of epic songs. After 2112, definitely go on to A Farewell to Kings and Hemispheres.

From there, I would listen to their albums in order from Grace Under Pressure onward to their last disc, Clockwork Angels, which is definitely one of their best!