Although this is probably private enough, you can opt out of measurements by turning off the Privacy Preserving Ad Measurement option. Essentially, the system makes it so that an advertiser knows only that somebody clicked an ad, not you specifically. You can also set Hide IP Address to Trackers and Websites. This setting will stop some sites from tracking you as you browse the web.
We suggest DuckDuckGo, which doesn’t track you or target ads. Change your default search engine: Google is the default search engine in Safari, but if you don’t like the idea of Google slurping up all your search data, you can change this (afterward, you can always head to if you need to) by going to Settings > Safari > Search Engine.