I want to create a whole family of related languages like a natural language family, like Semitic, Italic and Germanic languages. In what ways can this be done? What are the requirements, drawbacks and benefits of each?
The usual way to approach making a family of related languages is to first make a proto-language (or adopt an existing or reconstructed natural language for this purpose), then simulating natural evolution of both phonology, morphology and semantics in multiple different directions. While the creation of the protolang cannot really be parallellised (though one can deliberately introduce features that one would like to play around with in the following process, or that one can easily see multiple outcomes for), the process of evolving the descendants of the protolanguage can definitely be parallellised, and whether or not to do so is simply a matter of taste (though some things necessarily require some amount of parallel work, such as making a dialect continuum).
There are alternative methods to the derivation-from-protolang method, however they tend to either be much more cumbersome (e.g. trying to reconstruct a protolanguage from two or more seperate conlangs) and/or produce results that do not show the same regularity of correspondence that is indicative of genetic relation in natural languages (e.g. trying to just make two seperate but similar conlangs).
For a naturalistic language family one has to apply naturalistic sound shifts and other naturalistic language changes. Those rules and changes are usually directed, therefore it is the best to design the oldest stage of the language (aka the proto-anguage) first and to apply sound shifts and language changes afterwards.
Designing a whole language familiy requires a lot of historical linguistic background, but it is not impossible, as the family of Elvish languages by Tolkien shows.