I can share my experiences, FWIW. One was inspiration, the other calculation. Both worked.
For my first start-up, we purchased / licenses a dormant technology from a larger start-up. They had abandoned it as noncommercial. 12.5 months later, we sold for $50,000,000. The “inspiration” wasn’t the technology itself — that was already proven, at least at a very nascent stage. The inspiration was seeing changes in the market that meant it could finally be commercialized and sold.
Put differently, I “saw” the idea and the white space and jumped on it.
The second time, with EchoSign, it was more calculation. The founding team was just super excited about where the web was going, and we wanted to do something in B2B web back when SaaS was in its relative infancy. The white space was much broader and less specific.
We narrowed that down to an idea of “Flickr for Your Docs”. Then we picked different sub-ideas from that rough idea, and picked EchoSign. It could have been Box, or it could have been Apttus, or it could have been other ideas from that genre. But we had the most conviction around EchoSign, in part because it best matched our backgrounds. So we picked that one and built it.
So I think for me at least, I’ve learned both “the stumble upon one core idea and jump on it”, and the “carefully pick one from a genre”, both those strategies can work.
There is no single best path.