So you can probably sub divide that between 1080 and 1124 with the start of the reign of king David I. King David brought in significant regions of Normano-Scottish influence in the Scottish Lowlands. Particularly places that today are the Lothian counties and Berwickshire that had once been part of the the Anglo-Saxon kingdom of Northumbria prior to the Scottish conquest of the area and then under David saw settlement of Norman knights and English merchants in the new burghs towns he built.

Now although the military structures of feudalism affected the structure of how low status infantry was raised between the earlier and later periods in the Scottish lowlands in both cases the equipment has some similarity.

Your primary tools of the trade as is so common world wide is a spear and a shield. Scottish round shields would have been very much dominant prior to the Norman influence. These are not to be confused with later targes, they're generally larger, 60-75cm diameter, they sport a central boss and made of wood with a fabric cover where a targe was all metal or metal plated on wood. While round shields take a while to go entirely out of use more norman influenced kite shields do start to come into play in the associated low land regions, particularly these brugh towns after David. That's the larger tear shaped style shield. Infantry often wore gambeson jackets although Scottish soldiers were also more likely than many other people to wear a leather jack for armour. A knife of some kind is also likely to be carried as a secondary, if you have a little money something larger like a Saex or Longknife is possible. Generally its not till later that the average peasant or clansman can afford to carry a sword.

Similarly in both periods you'd have a slightly more professional force of infantrymen who'd often form the frontline. Sometimes these would be mercenaries, sometimes they'd be a more permanent retainer of their lord or Toisech clan chiefs. Again spear and shield is a pretty common set up generally, round shield for Gaelic-Scots, kites for Norman influenced or originating soldiers.

Though in many cases some of these slightly more professional soldiers had a broader variety of weapons they could pick from, hand axes and dane axes (particularly in norse influenced areas), swords (sometimes as a side arm), Long knives or Saexs (as a side arm instead of a sword generally although you might carry one as a side arm if your primary weapon is a sword to). But the main one is that they're much more likely to wear mail than lower class or less professional warriors particuarlly as you get into the late 12th century. And the later and more norman you get the more likely it is your mail is longer on the sleeves and thigh. This is usually worn over gambeson or occasional a leather jack. As such these guys often form the frontline of the shield wall where if the odd spear point should slip and graze them their armour will protect them, plus these more experienced men are likely to be better at keeping cohesion and more likely to stay steadfast.

For the nobility you probably see the biggest change. Prior to norman influence Scottish nobles almost always fought on foot. They'd be even more likely to wear mail, it'd be more likely to be longer on the arms and legs, they'd be more likely to be able to carry a sword as a side arm and be able to choose between that wide range of other weapons to carry as a primary. But with Norman influence came Norman knights. And Norman knights fight fought much more on horse back. Some Scottish nobles followed the fashions although Scottish nobles, particularly in areas with less Norman influence, fought on foot more often than many of their southern counter parts.

But where they're on horse back the primary weapon is a lance with a sword as a side arm. And the wealthiest nobles in particular can afford even longer mail going three quarters down the arm generally and maybe things like ventail around the neck and the like. While cavalry had occasionally been used before it now becomes more common to see in open battle as opposed to scouting, they're importing larger horses and it seems likely they're more likely to be using more aggressive tactics.