As a starting point I'd go all-in on serverless because even though it's not necessarily the fastest response times or cheapest, it does let you completely ignore several sets of scaling challenges till the price matters. So I'd go serverless for spidering, indexing and user-facing APIs. UIs I'd go static HTML on a CDN.

For database, first I'd lean on plain file s3-like storage as much as possible for spidering and indexing data and try to keep the user-facing database under a couple hundred terabytes, I'd probably favor some bare metal at this point but that will fit on some "db as a service" providers.