I'm vaguely planning six base colors for mine, then six lighter of the same, and six darker of the same, then a couple shades of "white" and "black".
Red (Pink, Crimson), Purple (Lavender, Violet), Blue (Sky, Navy), Cyan (Seafoam, Teal), Green (Spring, Forest), Orange (Yellow, Brown).
Not too concerned if you want to borrow any of that, because it's subject to change for me, too. While some colors are 'important' like Yellow, Orange, and Pink... no one really needs
three shades of them, necessarily. But if you find that your site needs more Pink, think on the same scale (Rose, Magenta), or Orange (Tangerine, Vermillion). More 'natural' sites may need a lot of Browns as well, along with delving into a whole slew of creamy off-whites, too.
Three shades of each may seem excessive, all the more reason to lump similar colors together. But I think light and dark versions are rather important. ^^
Obviously these may be too bright for use as is! But I suggest making a palette kind of like this, and then making sure colors look good across all species before locking them in. (This was my original copy, before I tweaked it a lot for my site.)