"My question is about how many figures am I going to need to represent an average WOR Army / battle in 28 mm?"
Depends on the rules, the figure representation scale and whether you want to fight complete battles or just skirmishes.
"Is there an upper and lower figure, different rule sets must use different troop scales?"
If you are talking about complete battles then:
1st St Albans: ~3,000 Yorkists ~2,000 Lancastrians
Towton: According to the chroniclers, both sides were about 30,000 (total of 60,000 engaged) but this is TWICE the size of any other WOTR battle and IMHO is wildly exaggerated. I would put them at about half that. Still the largest battle ever to have been fougt on English soil.
"Also I know little of the WOR army composition."
Neither do we, if the truth be told. All the chroniclers tell us the numbers of troops involved (but see above). There is little if any indication as to the mix of troop types.
"The main troop types were Archers and Billmen at a 2:1 ratio is that correct?"
No. As others have said this is more likely to have been nearer 1:1 based on the information we have from commissions of array and letters of indenture.
"What ratio were Men at Arms to other troop classes."
Lower than most people think, assuming you mean men in full harness.
"Will I need many mounted or did they always fight on foot."
Mounted combat was unusual in WOTR. There are a few examples, e.g. the "200 spears" at Tewkesbury and some of the Lancastrians at 2nd St Albans.
"Hand gunners, Canon and Crossbow, Spear/Pike Men are these rare exotic troop classes worth bothering about?"
Canon? No, the clergy kept well out of it
oh, sorry you mean artillery. Handguns and artillery were the new fangled weapons of the period, unreliable and often supplied by foreign mercenaries. The effectiveness of a fortified artillery encampment had been proved at Castillon in 1453 and in at least two WOTR battles (Northampton and 2nd St Albans) it seems that the same tactic was attempted. Handguns made their first documented appearance on an English battlefield at 2nd St Albans, although they were a miserable failure.
There is little evidence for the presence of crossbows, spears or pikes. Crossbows are not common in England, the warbow being much preferred.
"So what's an authentic mix of troop types in ratios which look historic"
You guess is probably as good as mine, but see other comments above.
"How do you integrate the figures to simulate the warfare by fighting in 3 battles on the tabletop?"
I am writing a set of rules that hopefully will achieve this. IMHO the rules currently available do not really do so (but then I admit I'm biased).
"Is there any sort of army lists reference online?"
I'm not aware of anything.
"I know if I bought a rule set this would answer all questions"
Not necessarily!
"but you guys have the hard facts."
Er
no. There is very little "hard fact" about the WOTR at all. Most of what we know is educated guesswork based on interpretation of the scant primary sources.