Byron has been a perennially fascinating personality since he lived, hence the number of biographies on him in print, but I wonder how many people have actually read his poetry?
This is a fine place to start. All the dramatic narratives are here: Childe Harolde's Pilgrimage, Mazeppa, The Giaour, Lara, The Bride of Abydos, The Corsair - as well as some of the famours lyrics such as 'So we'll go no more a roving'.
If you've never read Byron, then you might be surprised at the sheer narrative drive of these poems that keep you reading, even without the beautiful language. Always atmospheric (especially in the eastern tales) Byron for me has always been one of the poets with the strongest sense of musicality and rhythm in his writing.
Unfortunately the shorter poems and lyrics are in a separate volume, as is Don Juan, but this is a wonderful collection all the same whether you're familiar with Byron or not.
The Penguin volume has also been well-edited with notes, so it's great if you're studying Byron.
Altogether an excellent collection.