'Styles' is not the usual way to describe philosophical systems. Jules Vuillemin has written a short and rather technical book What are Philosophical Systems (Cambr. UP 1986) which comes close to such an approach as he used different 'manners' of predicating to classify philosophies and he even managed to construct his taxonomy as an a priori schema (summarised at p.128, shortly before the end).
What this technical exercise boils down to is well known: 4 types or styles of philosophy are thought to be possible as monism or dualism are combined with idealism and materialism. So there are pure idealism or pure materialism and also idealistic dualism and materialistic dualism. At the end of antiquity the 4 ways have already been explored as, e.g., Platonism, Atomism, Peripatetism and Stoicism.
In modern times this schematic division is seen as German idealism (Hegel, Fichte) v/s French materialists (Holbach, LaMettrie) and Cartesians v/s British empiricists.
According to Vuillemin, skepticism and eclectism are secondary methodological stances that should be seen apart from basic fourfold division.
Today the leaning toward idealism is seen as a 'continental' style while its alternative is the so called 'analytic philosophy'.
Otherwise, the shortest presentation of philosophical styles is given by various answers to the question 'why did the chicken cross the road'.