I paint a lot
of flowers. For achieving nearly every color you may wish, you really can't go wrong by selecting the 3 primary colors: Cyan, Magenta, and Yellow.
Cyan: Thalo Blue (PB15)
Magenta: Grumbacher Thalo Red Rose, OR W&N Permanent Rose 502 (both PV19).
Yellow: Winsor & Newton Transparent Yellow 653 (PY128)
These are all transparent colors, and to make them burst forth with their highest chroma, you will need to add White.
To that palette, you can add some useful colors, both opaque AND transparent, such as Ultramarine Blue, Cadmium Orange, Ivory Black, Quinacridone Red, and, as someone previously mentioned, Dioxazine Purple.
And, I usually mix my own Greens.
. And, I'm sure I must have used some Burnt Umber somewhere within that painting.