Why meditate? For all the reasons you mention, and more. To release attachment.
How? My tradition/school uses mantra chanting as our primary meditation form, with silent sitting as a secondary form; these are formulated as standard services. We also practice writing meditation, copying our mantra or the sutra(s), or occasionally the image of the Buddha. An individual is free to meditate in any form he/she desires.
When we chant, we recite Na Mu Myo Ho Ren Ge Kyo as our mantra. We also recite portions of the Lotus Sutra, either in english or in shindoku (Japanese pronunciation of classical Chinese).
Desired outcome? Peace, calm, rhythym, centeredness, wisdom, discipline, awakening, compassion, health, more.