HiWhere are you planning to be based? If you are in England or France, you're definitely going to be brigands - you'll be traitors in the english areas, and enemies in the French.
You could move to italy, where you could take service as mercenaries without anybody caring that much about who you want on the throne of england.
From a purely practical viewpoint, brigands doesn't sound that good an idea. A group the size of yours is going to get hunted down and killed without too much trouble at that time - you're well past the days of the big bands or marauding routiers that infested france after the peace.
Why is your group still loyal to Richard? Are you former retained men of his? If so, that gives you a lot of the setup information about your characters, as you'll then know what they were doing pre-1399.
If you weren't his retained men, but sympathise with him, I don't think you'd be wearing his badge - it's more like unit flash on a modern uniform than a general sign of support for his policies.
Regarding liveries....well, if you're brigands, you can wear what hell you like or can steal!
If you were retained men of Richard, you might well still be wearing clothing issued to you while you were in his service. However, this need not be uniform - "livery" means that it is issued to you as part of your pay, not that it is in particular colours.
The same goes for any other commander - retained men were normally issued clothes (or a quantity of cloth to be made into clothes) as part of their annual salary, usually twice a year. This might be any colour the commander choses, and may simply be whatever's available at the time, and/or different for different individuals.
However, there are also accounts of lords dressing their entire followings alike, when they wanted to put on a good show.
As to what sort of individuals would be in such a unit....well, again, if you're brigands, anything goes! You have accounts of brigand bands being led by knights, rogue priests, all sorts - this is actually why Mallory is in the tower when he writes le morte d'arthur, for carrying on like a medieval Jesse James. Most will probably be archers, though, since that's what most of your troops are likely to be.
If you are still an organised military unit, well, armies at that point are basically being recruited by contract - X agrees to attend a certain lord for a campaign with so many mounted men at arms and so many archers, in return or a certain sum - and I'd use that as a guideline for what your unit should look like. Usual ratio is about 1 man-at-arms to 2 archers, but can go as low as 1:1 or as high as 1:3.
Men at arms are in full armour and riding "covered" horses, archers in as much armour as they want to wear and can afford - some of the illos from that period show them in damn near full harness.
Followers - well, depends mostly on setting and who you are.
Hope that helps
Neil