Officially Charles II succeeded his father, Charles I, from Charles I's execution. In fact the interregnum of the Commonwealth intruded, which is why the period of Charles II reign after he was restored to the throne is known as the Restoration. Charles II was known for his dissolute ways - it was said that any vice was tolerated at court except hypocrisy - and extravagant dress. Which bodes well for his hats!
This black velvet hat is more upright than the hats we saw for Henry VIII and Edward IV. There is a distinct band and a jeweled decoration. The plume, as we might hope from a cavalier, is large and colourful. The long black curls that Charles sports is probably a wig; after 1663 his hair turned grey and he began to wear wigs.
Here is Charles wearing robes of state and a crown. The crown is wide to my eyes; it looks like the crown on the back of a 5p or 20p piece, but stretched sideways.
Here we see Charles going about his business, being presented with a pineapple. This broad brimmed black hat appears undecorated. For shame!
Although helmets were still worn in battle, advances in gunpowder weapons had changed the emphasis away from armour and towards speed and mobility. As a young man Charles fought in the English Civil War and would have worn a breastplate and thick leather boots. Whether he would have worn a helmet or a plumed hat at a rakish angle I have not been able to find out.
 Having killed the king, the English parliament then banned the acclimation of a new king. However they were unable to agree a new constitution so to prevent the tyranny of a perpetual parliament, Oliver Cromwell launched a military coup. After Cromwell's death, still unable to agree on a constitution, the monarchy was reinstated.
 But before his execution.
 As all cavaliers on screen or in pictures do.