Something that is valuable has considerable monetary worth or is particularly useful for a specific purpose. This adjective is often used to talk about things that offer or may one day offer a material advantage or quantifiable benefit. Something that is invaluable has value beyond calculation or appraisal; it is priceless. Here we get into things so important or meaningful, such as the support of a dear friend through a difficult time, or yielding benefits of such great magnitude that they defy measurement or estimation.
Something that is common is widespread or universal. Something that is prevailing is generally current and supersedes others of its kind. The key difference is the suggestion of predominance. For instance, a prevailing view on a matter is a view that has taken over or displaced other views. A prevailing fashion is one that has caught on and emerged as the most notable or influential at a particular time.
To cultivate something is to tend to it and help it flourish. This verb is widely used to talk about tilling fields and growing crops. However, as a synonym for the more general verb develop, cultivate veers into metaphorical gardens: when we cultivate talents or skills, we refine them, perhaps with lessons or practice; when we cultivate relationships or friendships, we encourage and promote them; and when a celebrity cultivates an image, they are carefully crafting a public persona.