I have a long-standing fascination with the cochineal bug-pretty little silver mamas that yield vibrants reds, purples and pinks.
I personally love the pinks and purples which in my experience are the easiest to achieve-no cream of tartar, chalk, etc. Just an alum bath, time in the buggy pot and a nice wash-perfect. I have learned that one must filter all the bits and pieces out to get the best, or clearest, results. But if one is going for the purple blotches on purple, then don't bother filtering-it's all beautiful.
I like to use exhaust baths with other dyes to see what colors are achievable. It's not a scientific way to create color because of the inconsistencies but for one-offs, its a great way to eliminate waste. reuse reuse reuse, right??
Cellulose fibers, aka plant-based, could use a chalk afterbath to create bright, clear colors. While I love some bright jewel tones I LOVE dusty, muted tones. Below is an example of woven cotton and linen (top). Cellulose fibers in general need more dye than their animal counterparts.
Peace, love and dye on!