Modern chemical dyes can produce a very wide range of colour-fast shades without great expense. The vegetable dyes used in medieval Europe were much less versatile and (at the time) much more expensive. Choice of dye colour is linked to the status of the character you are protraying. The cheapest dyes (those most available to the poorer sections of society) are the least colour-fast, i.e. they initially appear quite bright, but very rapidly fade as the dye washes out. More expensive dyeing (using better fixing agents (mordants) or repeated dye-baths) produces stronger and longer-lasting colours, but should be restricted to high status characters. Dyeing vegetable fibres is particularly difficult.
A full guide on dyeing is available for download, including a number of successful recipes 
Photo credit Julia Kuivenhoven
Colour is a case where what you see at a distance isn’t always what you see up close. For example wool with contrasting colours woven horizontally and vertically can use authentic red and blue to give the impression of an otherwise inauthentic strong purple. Similarly, the ‘black’ wool of monastic habits was usually a mixture of dark grey, brown, black, white etc.
The following picture shows a range of the colours which can be achieved from authentic dyes.