Hmm. To get a good one-album grasp of what Living Colour is about, I'd go with Time's Up or Vivid.
Vivid was the debut and biggest seller, on the strength of "Cult of Personality." But I think Time's Up has the overall better songs throughout.
But either of those is a good first step.
If you like those, then let me know, I'll steer you further. Whoever said Stain (third record) is heavier, is correct. But Vivid and Time's Up are probably better representations of the band's core sound.