The web archive is a comprehensive backup of the web looking as it did in different points of time. Think of the web archive as a flash drive that you might carry around to keep important business documents on hand, or that term paper that you wrote the night before it was due! Now scale this little flash drive we’re thinking of up about a hundred billion times, and you’ve got yourself a web archive! The mission of the web archive is to store the internet in its entirety at different points in time over the last 15-20 years (or however far back the archive goes that specific page you’re trying to view). Although it is not a foolproof list, there can oftentimes be a plethora of content on a page that you mightn’t thought had fallen by the wayside years ago.
Should you consider hosting page from the wayback machine and bring it alive? What about shared hosting? If this is your first website and it’s relatively small, a virtual shared server is probably good for now. If you’re moving a large website which already gets thousands or millions of views, shared probably won’t cut it. Therefore, you should probably search for dedicated hosts or use a service like waybackmachinedownloader.com. They recover whole websites from the archive at once.
Stick with a provider that’s in the same country as your target audience. If your target audience is Americans, stick with a hosting provider that’s located in America.
The web archive and the Wayback machine are somewhat synonymous, so for all intents and purposes, you needn’t make a differentiation between the two. The Wayback machine is simply a branded name for the Web Archive, and is well known amongst individuals on the internet who have he desire to restore lost content.