Hi Miller,For an excellent introduction into the English soldier in the 15th c., I would recommend to you as a must read "The English Soldier in the Wars of the Roses", by Andrew Boardman. It gives a great insight into the tactical system employed by the English, and the equipment & orginization, and even an examination of the battlefield experience. It is not a flawless work, but it is the best overview available to date.
Jeff, Dave Key, and myself all have some problems with some of the conclusions Mr. Boardman draws, but it is still an excellent book - reallyu a pioneering book on the subject. It is in Print, and should be readily available online through Amazon or Barnes & Noble.
Adressing the Burgundian service aspect of your question is more trickey. Lots of primary documentation exists. Most of it is locked away in the 'Public Archives' in Dijon and the University there, written in middle French & Church Latin, and it is tough to access in any form. For easily available general information - much of the information taken from these sources try "The Armys of Medieval Burgundy" (Osprey publications Man At Arms Series), and Ospreys warrior series #11 "The English Longbowman 1350 - 1525(?)".
English bowmen could be found in Burgundian service from the alliance of Burgundy with England immediately following the assasination of John the Fearless, until the end of the Burgundian house of Valois in 1477 (and beyond, as Richard III gave his sister Mararet permission to hire bowmen for Maximilian & Mary of Burgundy's wars against Louis XI to retain the Burgundian Low Countries in the 1480's).
An interesting portrayal you might consider is the English Archers of the Ducal bodyguard - not an easy impression, but an impressive one. Phillip the Good had over 100 of them, and Charles by the end of 1473 had over a thousand of them. They would be a spiffy portrayal - look for Gerry Embleton's reconstruction in the colour plates of "The English Longbowman".
Bodyguard troops such as this would wear near a full armour (going by pictures of the Scottish archers of the guard of Charles VII & Louis XI) - complete plate limb defences, a brigadine - with either brigadine pauldrons or a light mail shirt underneath - the sleeves providing the shoulder protection, a mail standard (gorgerin) and an open or visored sallet. Their livery would be of a cloth & quality higher than their station would normaly warrent - reflecting the magnificence of their masters wealth & taste.
They would have been armed with a bow, a sword (either a bastard sword by the ordinances or an arming sword), and a glaive for guard duty on foot, as well as the omnipresent ballock or rondel knife. The Scottish archers of the French kings which the Ducal guards were apparently a close copy of also had bucklers (you can't wear gauntlets & shoot.)
The Bodyguard archers obviously filled the role of guards for the Dukes person. They also were used as guards for the Marshal of Burgundy, and were used as elite troops in combat - a detachment being sent to guard an important terrain feture during the battle of Grandson.
If you have only a few people - not enough for a lance, then this could be an interesting portrayal. They are nearly as well equipped as a man at arms (As a matter of fact, an officer commanding would probably be equiped as knight, if not actualy one - which he well could be), they look very spif, and they could fit into nearly any camp with Burgundian troops. Heck - you could even guard AM's tents if you made it out her way, as Antoinne, Grand Bastard of Burgundy usualy had a guard of them, being for quite some time Marshal of Burgundy. They also pre-exist the companies of Ordinance, and co-existed with them until the fall of the Duchy, so it would be a flexible portrayal timewise, so long as your equipment pre-dates (say 1450's), you would be good to go for the whole run of 27 or so years.
The standard of the archers of the bodyguard still exists (captured at Nancy), and a photo appears in "Die Burgunderbeute". 
In 1473 Sir John Middleton commanded an entire company of the Ordinances that was composed of Englishmen.
Sorry for the long winded ramble !
------------------
Bob R.