If you are a web developer or are familiar with web terminology like origins, domains, frames, XHR, etc on the web, and are willing to put in some time learning how to use it (15 mins for a seasoned web dev, maybe 30-60 mins otherwise) get uMatrix (https://github.com/gorhill/uMatrix). It will change your life! If not, use ScriptBlock on Chrome or NoScript on Firefox. Block all scripts (and if using uMatrix, cookies, XHR, and frames) by default and whitelist as you go for sites you trust (or want to use bad enough to potentially open yourself up for tracking).
JavaScript developers should ask themselves if they want JS to become the popup of the 2010s: initially well-intentioned, shamelessly abused, universally loathed, and ultimately killed.
My suspicion is that fingerprinting by the core domain will actually get worse since your browser behaves so differently from stock browsers (which is after all the point of uMatrix :-) ). The majority of trackers tho will be third party (such as Google analytics). Very few sites roll their own trackers because it's hard to get right, and some great ones like GA is free. For those that do, I'm not too worried anyway, but that's certainly just a personal thing.
However, it comes with a fairly long list of downsides: less secure than Chrome, less secure than even Firefox it's based on because it's not updated as often and quickly, and you MITM yourself by default, and it's slow, it doesn't block ads... The price to pay is steep.
I'm using a VPN + ublock origin + https everywhere + temporary containers + don't track me google + chameleon + canvas blocker + custom user.js (that disables e.g. webgl).
It's pretty good to address many tracking methods (e.g. cookies, IP) but fingerprinting is remarkably hard to prevent.