But is a private instance really that private? Because all your searches must be bundled together and perhaps some of those searches include personal data. I am asking as it is something I have genuinely thought about for some time

I use Firefox and the arkenfox user.js, which is not an extension, but helps with privacy. For the extensions, though, they are as follows:

• uBlock Origin // on medium mode (Check out what blocking modes are if you don't know them already)
• LibRedirect // to redirect to more privacy respecting frontends
• Skip Redirect // for increased privacy in terms of redirects
• Smart Referer // on strict mode. I use this as I have set network.http.referer.XOriginPolicy to 0 as 2 was a little too strict for me

I think more extensions than these would probably hurt my setup. I have followed the advice from the arkenfox wiki. Check it out if you want to look into a more private and secure Firefox configuration. Also feel free to criticize or ask questions about my setup :)

If I wanted a browser fork from another company I would just choose Mullvad Browser. At the moment, though, Firefox with arkenfox.js and uBlock Origin will do