The official policy of Google, is "No data shall ever be deleted, but retained in perpetuity".
In other words: Even if you manage to "unsubscribe from Google and all its services", all records of your visits are retained.
If you want to use a Search Engine which is free, anonymous with all records deleted within 24 hours, you may use Firefox, and the Scroogle add-on.
This enables you to use Scroogle Search Engine, to anonymously search Google, so you can see the results in your Browser, but Mr Google does not know your IP address.
Then you can choose any link, and go there direct.
For use without using a Scroogle Addon to Firefox Browser: