Spectrum is a jQuery colorpicker plugin that probably comes with all the features you are looking for.
It is image-free (only CSS and JS) and can be used for all browsers or only as a polyfill for the
input[type=color] of HTML5 .
The picker is actually familiar to designers/developers as it is the same one that comes with WebKit DevTools (created by the same developer) but now available as a jQuery plugin.
It has support for color palettes by storing/displaying the colors you chose, the default selected color can be set or it can be configured to only display the palette with pre-defined colors.
Alpha transparency selection is available, can be always visible (without clicking to a picker icon) and supports multiple color formats.
Spectrum can be customized with CSS and it works on mobile as well.
Compatibility: All Major Browsers