So has anybody done any research on this or is everybody just guessing? My google searches have revealed very little. I see a couple of essays claiming that swords were the most common but they don't back that information up with any evidence. Other sites claim that bows were the most common medieval weapon as they were cheap and more practical. One site even claimed the bil was the weapon of choice. Not much mention of spears but I would surmise that they were primarily anti-cavalry weapons, atleast in medieval times.
I can't provide a source, but logic alone dictates that spears were the most common weapon. They're cheap, fast, have range, pierce, work well in formation, stand up to cavalry, combine naturally with a shield, and comparatively easier to learn to use. However, we should distinguish between battles and the personal combat that takes place in TES. Most armour in TES is plate, so we should be seeing maces, pickaxes, other polearms, and two-handed swords being used - and no shields (if there is ever a realistic damage model).
the common infantry usually had crappy armor/weapons
There is no logic to this statement. If you were going to war, why would you go poorly skilled and equipped, or take poorly skilled or equipped men? Common soldiers were very often professional or semi-professional.