Permanent searchable web archive

Total newbie here, but here’s what brought me here. I currently pay a host for a website, and I envision a day when I will no longer be here to pay for or update a site. As I understand it, I can record my site at one point in time. Now, how to perpetuate the ability for someone searching for a key word or my name to obtain my archive. Is a domain name necessary or a pinning service? Domain names can be purchased for 10 years, or potentially longer. Not clear how long pinning services like Piñata can be purchased? Of course, there is a question as to the durability of these. I’m not looking for 1000 years, or even 100 years, but somewhere in the 20-30 years, ie one generation would be acceptable. Are their options to make a web archive searchable that fit? Thank you.