There were very few true knights at this time and the bulk of cavalry on both sides would have been made up of younger sons, sergeants, squires and mercenaries.  Knights would wear a long mail coat or hauberk and may also have worn a coat of plates (leather or padded fabric reinforced with metal plates). By the middle of the thirteenth century the knight's arms and legs would have been protected by mail and he would have worn a mail hood or "coif" over a padded "arming cap".  Other cavalry would have worn lighter, simpler or recycled armour.  Knights would have worn a surcoat over their armour with their coat of arms applied to the surcoat.  Their arms might also be present on the covering or "barding" for the horse. Other horses would have had leather barding.

Helmets would have been plain open-faced, or flat-topped or the well known barrel-shaped great helm.  The trend towards smaller shields continued during this period with the large kite-shaped Shields characteristic of the Normans giving way to the later medieval "heater" (triangular) shield, although all sorts of shields, antique and up to date, would have appeared on the battlefield. Plate armour was sometimes seen, often used to protect the knight's knees and elbows.  Plates of armour might be made of boiled leather instead of metal.

Sergeants (from the Latin for "servant") were professional soldiers trained and experienced in the horseman's skills. They tended to be better protected than infantry though not as well protected as the knights.  They generally wore mail hauberks - maybe shorter than the knight's - and, like the knights, would fight dismounted and would ride with the knights.  They bore no coat of arms (although they may have worn a lord's "livery") and horses were usually undecorated and unprotected.

Mid-thirteenth century armies consisted mainly of infantry and spearmen of one kind or another were the main type of infantry of the day.   Spears, bills and axes were carried.  A professional infantryman would wear mail if he could afford it but would certainly wear a quilted leather "jack" or jerkin made of metal plates rivetted to a quilted fabric garment.  Helmets were open-faced, wide-brimmed kettle helms or simple "pots". 

Longbows were found (more among the Welsh than among the English) but the doctrine of massed archery that won Crecy and Poitiers was in the future.  Bowman - longbows or shortbows - wore little or no armour.

Peasant levies were often armed with improvised weapons (a felling axe, a scythe or a pitchfork made a serviceable weapon) and a may not even have worn a leather jerkin.  Some peasants may have been armed with bows.

Town "militias" would have had some drill and have been more willing to fight than peasants, having more to protect. Their appearance would be similar to rank and file infantrymen but with poorer equipment. 

Crossbowmen were the most common missile-armed soldiers of the day and both sides are likely to have used some. Crossbows were expensive and the province of mercenaries, so the crossbowmen would be at least as well equipped as regular infantrymen.