In what way could this considered to be “your own internet archive”? I see no way to register a user and save pages to a collection.

If you really want to create your own archive, set up a Live Archiving HTTP Proxy[1], run SquidMan [2] or check out WWWOFFLE[3].

If you want something simpler, have a look at Webrecorder[4] or a paid Pinboard account with the “Bookmark Archive”[5].

[1] http://netpreserve.org/projects/live-archiving-http-proxy/

[2] http://squidman.net/squidman/index.html

[3] http://www.gedanken.org.uk/software/wwwoffle/

[4] https://webrecorder.io/

[5] https://pinboard.in/upgrade/