@Chris
Alizarin Crimson is not lightfast so it's better to go for Permanent Alizarin Crimson. I don't use Perm Alizarin Crimson so I can't compare it with Quin Red and Carmine. A nice cool red to have is Quin Rose or Quin Lilac. Check out Jane Blundell's blog for more comparisons.
@Chris
Alizarin Crimson is not lightfast so it's better to go for Permanent Alizarin Crimson. I don't use Perm Alizarin Crimson so I can't compare it with Quin Red and Carmine. A nice cool red to have is Quin Rose or Quin Lilac. Check out Jane Blundell's blog for more comparisons.