Best way to source components
Start with the datasheets for the key components (also application notes and evaluation board documentation packs), chances are good that a reasonably competent engineer has already done much of the work for you and a reference design or &quot;typical application&quot; schematic is provided, perhaps with actual part recommendations for critical parts (such as the inductor in a switchmode supply).
To the degree you come up with something novel or modify the reference design, your understanding of component characteristics and non-technical factors may come into play. For example, I may choose a particular inductor because it is shielded, because it is easily available overnight  (or there's a reel sitting in the stock room), or because it is multiple-source and inexpensive for the PCBA house to source in Shenzhen. Maybe all factors are available at once, but more often there are trade-offs to be made.