The swartzchild metric, the kerr metric etc. where constructed with specific goals in mind, how does one go about doing that with goals in mind? Any help or comments appreciated. I don't expect a guide, I doubt one exists,
Exact solutions of the Einstein field equations are notoriously difficult to find. In the almost 100 years since the EFE's discovery by Einstein, only a select few physically pertinent exact solutions have been found. There are whole books written on this subject (see e.g. https://www.amazon.com/dp/0521467020/?tag=pfamazon01-20), and there are several different methods worth trying. As an introduction, I might recommend Wald's "General Relativity" chapter 7.