Often falling squarely in the "Love Them" or "Hate Them" category, Rush is simultaneously overrated and underrated. They're overrated often by their own often over-zealous fans ("They are the three best musicians that ever walked this earth!") and they're underrated by those who refuse to give them a fair chance ("Geddy Lee CAN NOT SING!"). Neither of the two examples of comments I've just made are correct. They are not the best musicians ever, and Geddy Lee most certainly can sing. Therefore, if you're thinking of getting into Rush from a long time fan (15 years), read on.
There are several live albums and best-of collections out there, but I'm going to stick to the studio albums. Moving Pictures is almost universally considered their best work, by hardcore fans and casual fans alike. It contains the rock radio hits "Tom Sawyer" and "Limelight," as well as staples such as "Red Barchetta" and the instrumental powerhouse, "YYZ." It also contains what would be one of their last extended, proggy tracks - "The Camera Eye" & what would set the stage for most of their 80s work - the synth-laden "Vital Signs." If you like _Moving Pictures_, you're sure to also love the album that preceded it, Permanent Waves. _Permanent Waves_ was a distinct turn in approach for Rush. After spending the 70s mixing Zep-influenced rock with Genesis/Yes/ELP prog, _Permanent Waves_ is stripped down (for the most part) catchy, yet complex, rock songs - "The Spirit of Radio" and "Freewill" are still played routinely on rock radio. It also contains the extended cuts "Jacob's Ladder" and "Natural Science," the latter of which always lands in most hardcore fans "Top 5 Rush Songs." If you like these two albums, the next one I would suggest would be my personal favorite, Presto. Many fans are divided on _Presto_ but it is unlike most of Rush's other albums in that it pushes songwriting and production to the forefront rather than in-your-face chops. It's not as heavy as their earlier albums, but it is their best batch of songs and contains Geddy Lee's best performance as a vocalist to date.
Ok - so where to go from here? Easy. If you like the longer, musically-complex, rock side of Rush, buy Hemispheres, A Farewell to Kings, and 2112. This is Rush at their proggiest - but hardcore fans of progressive rock of the 70s (Yes, King Crimson, Genesis, ELP) often cite Rush as being far from in the same league as these groups in terms of composition and inventiveness. I don't entirely disagree with this view, but these three albums are strong and contain a number of great moments, and just a few that have not aged very well. Now, if you *really* like these albums and prefer Geddy's screeching as opposed to his later day singing, you might as well pick up the first three Rush albums - Rush, Fly By Night, and Caress of Steel.
Ok...now if you find yourself gravitating more to the 80s/keyboard era of Rush, you may want to make some different choices from the ones mentioned in the paragraph above. If you like Rush using keyboards and synthesizers, Power Windows would be your best bet. If you love _Power Windows_, follow it up with Signals, Grace Under Pressure, and Hold Your Fire - three albums where keyboards play just as an important part as the other instruments.
Now, if you want some contemporary Rush (1990-present), I'd say Counterparts is Rush fitting in nicely with the grunge/rock movement of the early 90s, Vapor Trails is Rush showing today's bands how to rock convincingly, and Snakes & Arrows is truly an excellent work--one of my favorite Rush albums of all time. Quite a feat for a band doing this for nearly 40 years. It takes the chunky rock of Rush's releases since 1993 and adds a 'classic' touch of their 70s work.
There's only one Rush album that I wouldn't recommend Test for Echo, which I consider Rush on autopilot - some good moments, but very underwhelming and offering nothing new whatsoever. Roll the Bones came out during a weird time for music - late 1991 - and the thin production bogs down some very good songs. This album also gets some flak for the 'rap' that comes in the middle of the title track. Keep in mind - this was 1991.
So, good luck with your quest of all things Rush! Once you start to become a huge fan--and I know you will--pick up their excellent new documentary Rush - Beyond the Lighted Stage [2 DVD]. I think they are often overlooked as great songwriters because so much of their early stuff was much more about rocking out in weird time signatures and exploring science fiction, fantasy, and folklore. My favorite era of Rush is 1980-present as opposed to the 70s.