The Pict cavalry were famed and fierce and we can see them commemorated in victory over the north British or possibly the Northumbrians on the Aberlemno Stone. We note that, unlike their foes, they lacked armour, light cavalry then in the popular view.
They would, by virtue of owning horses and swords and spears, have been drawn from the nobility. Thus they had the time to practice their skills both martial and equine. Frequent combat experience via raiding, defending and outright war rendered them formidable foes. It is likely that the Pict nobility was a numerous and slightly richer rather than a smaller and much richer elite segment of wider society.
At some times and in certain places some of them may have had armour but it is unlikely that it altered their mode of combat. So far as I can tell that was to hit and run and hit again. The scholar Philip Rance's thorough treatment of the word Drungus and its Celtic origin, the etymology of the Irish term Marc Slua, Caesar's comments on earlier British cavalry and the evidence in Brythonic and early Welsh heroic poetry all seem to me to support that view.
Chariots were also available in smaller numbers. They were expensive requiring two horses and two men, only one of whom could fight. As well as the outlay on construction and regular maintenance of the vehicle the driver also required his keep and suitable rewards.
The chariot was partly a wealthy noble’s status symbol but it had other advantages. It was a highly manoeuvrable missile platform holding more javelins than a horseman might easily carry and it could deliver high quality warriors, albeit in small numbers, to just where they were needed and extricate them at speed. It was very vulnerable to good cavalry. The Picts eventually gave up on the chariot but there are some quite late references to British chariots so if you like them, use them.
The images we have of Pict infantry show men with spear, or occasionally sword, and shield and archers and crossbowmen. We can only speculate on the tactical role of the missile men . They may have skirmished or supported the cavalry or the infantry or all of those things.
The biggest group in the army would have been spear men. The images carved into the stones suggest- no more than that- men who fought in formation. These would have been the free men of the Picts performing their required military duty. I tend to see them as forming up in blocks around which the other elements of the army operated. Gildas writes of "swarms" so we might be thinking of large numbers here.
The scholar Charles-Edwards thinks St Patrick’s letter to soldiers of Coroticus indicated the presence of a pagan warrior cult among the Picts. There are precedents and if you share the view a single unit of high ability and high morale foot warriors would be appropriate.