Sandra, if you want to branch out from the compilation CD (which one is it, by the way? Hot Rocks or something else?), consider these 5 albums: Beggars Banquet (Nineteen Sixty-eight), which besides Sympathy has great tracks like Stray Cat Blues, Parachute Woman, Street Fighting Man, Salt of the Earth (Keith's first vocal, I think, and he screeches out the first verse like some kind of constipated junky -- great moment); Let it Bleed (1969) -- Shelter, the title track, You Can't Always Get What You Want, Midnight Rambler, You Got the Silver, Monkey Man; Get Yer Ya-Yas Out! ('70) -- the 1969 live show from Madison Square Garden, one of the great live records in rock, and the best live Stones recording; Sticky Fingers ('71), with Brown Sugar, B*tch, Wild Horses (I like this one myself), Sister Morphine, Dead Flowers, Moonlight Mile; and the Stones' true masterpiece, Exile on Main Street ('72). A double album with not a weak moment on it.
These five consecutive LPs are the peak of the Stones' career. I don't think that even the Beatles or Led Zeppelin strung together five straight albums of such high quality.
However -- it may take more than one listening to appreciate these records' greatness. Exile on Main Street, which usually is ranked in the top 5 or 10 albums of all time (in various magazines/books/polls), was actually panned by many critics when it was released. The Stones aren't as easily accessible as the Beatles; you may listen to one of these records and think 'eh, not that impressed,' but if you put in the time, it'll be worth it. They'll grow on you.