Hi Dirk... there is not actually a definitive answer for all that, just some conventions that were followed somewhat loosely. I have used illustrations from Citadel Six's site, so apologies for the watermarks.
BannersEach knight or other person entitled to bear heraldic arms would have a banner displaying those arms, the size and shape determined by his 'rank', which conformed to those in the rest of Europe. These served no function other than to mark his presence on the battlefield.

Earl of Ormond's Banner.
'Retinue' StandardsIndividuals who were hereditary knights (not knights for 'life'), lords, earls and dukes, usually had permission to issue liveries and badges to their household, servants and any men they led in wartime. A personal standard with that livery and bearing his badge(s), would also accompany such an individual, again to mark his position to his followers and to serve as a identifiable rallying point. These standards appear to have been 'swallow tailed'.

Earl of Ormond's Livery Banner displaying badges associated with him. There also seems to have been smaller single-tailed pennons in use, which may have been used for sub-sections of the household and permanent retinues (like later cavalry guidons).
'Company Standards'Traditionally English units were divided into groups of 20 and 100. From muster rolls of the Hundred Years War, it seems that individual bodies of men raised by an individual of 'around 100 men' carried a standard. It is possible that individuals who raised large numbers of men identified each group of around 100 with one of their badges.

'Company Standards' based on the Earl's badges.
Apparently livery badges were hereditary within a family and associated with a title possessed by that family... so The Earl of Ormond had one for that title, another for being the Earl of Wiltshire, another for Lord of Wherever and so on.
Livery colours seem to have been changeable on the whim of its owner. John Howard as Lord Howard chose black for his followers initially, then went to blue when he became Duke of Norfolk. In 1483-4 his household men were still in blue, but he was also buying a lot of red and white cloth (the cheapest colours) presumably for the men he had promised to raise for King Richard III.
Anthony Woodville changed the livery of his servants every day through the course of a week long tournament. Lord Maltravers was another who liked black, but when he became the Earl of Arundel he changed to Red and White (as opposed to his father's plain red)... a few others did similar things.
There is a book by Freezywater publications "Standards, Banners and Livery Colours of the Wars of the Roses" (or something like that), which is fairly inexpensive and packed with standards. It may have the odd error, but it is perhaps the most comprehensive and closest to the mark for my money.
I don't claim the above as the complete and concise guide to banners and standards... it's just how I understand it.