If you crave the “old” web there is also gemini (wiki)
https://geminiprotocol.net/
Even if you want to filter all pages with adds you still need to index them so you would need a considerable amount of storage at “1 million web pages requires 28.6GB” (open-source-search-engine/html/faq.html at master · gigablast/open-source-search-engine · GitHub) and there are trillions of pages out there and storage will scale more or less linearly (though once you need to shard etc. you will have to provide more for overhead).
As for compute that is a lot harder to guess, but the big cost is probably storage.