Varna-Yoga
It is interesting to note how well the four varnas match the four broad categorizes of yoga (jnana, raja, karma, and bhakti). Note that none of these were mutually exclusively (in fact in the past all forms of yoga were accompanied by a good amount of bhakti).
It is said that the difference between the kshatriya and brahmin in terms of approach to knowledge is that the former can be single pointedly focused whereas the later is more broad/knowledge-oriented.
The focus and determination of a kshatriya made them out-skill others in areas that require extreme focus – like raja yoga (meditation/focus). Thus it shouldn’t come as a surprise that Krishna chose Arjuna as his point of focus, not to mention Krishna, Rama, Buddha, Vishvamitra, Kannappa Nayanar,… some of the most important spiritual figures in Hinduism all started off as (or are depicted as) kshatriyas, attaining the state of brahmin varna by virtue of self-realization.
The knowledge-orientedness of a brahmin made them out-skill others in areas that require depth of knowledge – like jnana yoga (higher-knowledge/wisdom). Examples are: Sri Ramana Maharshi, Sri Ramakrishna Paramahamsa, Siddhar Bhogar, Adi Shankara, Ramanuja, Madhavacharya, Sri Raghavendra,…).
The desire “to do/make” nature of vaishya made them best suited towards karma yoga. The humility of those of a shudra makes them best suited towards bhakti yoga. Many great saints and sages have been produced from these varna as well (Tiruneelakanda Nayanar, Nammallvar, Tulsidas, Kabir, Veda Vyas, Valmiki, Narada Muni, Mata Amritanandamayi,…)