Classic Blues tone happens when you ride the threshold between clean and distorted sound. This means pushing your amp hard enough that it just starts to distort. Then, hard pick attack can push it over the edge, while picking gently results in a clean tone. This allows for very expressive playing.

You can't truly get this tone from a pedal, because the tone comes from distortion in the power section of the amp. Which means playing loud. Pedal distortion, or distortion generated in the preamp, tends to be a lot less responsive to picking dynamics. You can try something like a Boss OD-3, which is designed to overdrive the preamp tubes.