Sibelius is, I believe, one of the most distinctive and original composers. If all you know is his 2nd Symphony, you cannot say you know Sibelius. In fact, each of his 7 Symphonies are so different from each other...one of the most varied cycles in all of music, I think. The Symphonies and the major tone poems (Tapiola, Pohjola's Daughter, En Saga) are all good places to start exploring. I think if you hear the symphonies and the tone poems, you begin to get a very clear picture of the composer's sound world, and then you can move on to the songs, piano works, etc.
As for the 2nd Symphony being clumsy at times, I do not see that at all. There is a sense of direction and momentum in this work that I feel is lacking in the music in other composer's in Sibelius's time. This is another reason why I love Sibelius. If find, for the most part, the music has a point and purpose.