The bright purple, for example, is a 2:1 ratio of Chinese Red and Brilliant blue.
Black = Better Black
The teal in the same picture = Kelly green + Brilliant Blue 4:1
Grey = Grey. You could water down black for this.
************************
If it were *me* I would buy a set of:
Chinese Red (or Fire Red)
Kelly Green (because green is hard to match for me)
Lemon Yellow
Brilliant Blue
Black
Soda Ash
Squirt Bottles
Urea (so you don't get speckly reds)