Tracking on the web is pervasive but by using a selection of browsers on Android it's possible to mitigate the main effects of this to enhance your privacy. This is an outline of the set-up I currently use which offers different options on the privacy-convenience spectrum whilst still being easy to use in practice.
I rarely use Chrome, typically it's reserved as a last resort in incognito mode for sites where the developers are of the belief that "people who don't use Chrome shouldn't be allowed to use the internet". However, it's far more likely I simply won't bother with that site.
Firefox is my main browser - by that I mean I use it for sites where I want to maintain a persistent session or want to refer back to them periodically.
If I'm doing a financial transaction I'll normally use Firefox, typically in private browsing to keep the data leakage to a minimum at the point it's most profitable (i.e. most likely and most promiscuous). If I'm feeling particularly paranoid I'll use a VPN to connect to my home network to keep suspicious activity detection systems happy.
* Yes, Ghostery does track you to a certain extent. However, in this particular situation I'm happy to trade down to their tracking to get better protection - after all I'm using this browser for sites where I'm logged in so, in this set-up, I'm explicitly opting in to tracking anyway by using this environment.
Firefox Focus is the browser I use most. This is a minimal - private mode only - browser, with built in ad-blocking, that can be easily reset to destroy history, cookies, and any other session storage: when I finish looking at something it's gone.
For additional privacy I route this browser through Orbot (Android's Tor client) meaning that there's very little about what I view in this browser that can be tracked.
The price for anonymity using Tor is that it's slow and some sites (Google, anything behind Cloudflare, &c.) don't play nice with it so sometimes I will want to browse using the device's normal internet connection. Orbot operates at the app level so, rather than turn this on and off for Firefox Focus when I want a normal connection, I use DuckDuckGo's browser which isn't routed through Tor. Like Firefox Focus, this is a private mode only browser so when I'm done with a site the session is destroyed.
Not strictly a browser but I use Talon as my Twitter client. This is also routed through Tor and I use Firefox Focus to ensure outlinks are also routed through Tor. Admittedly Twitter will still be collecting data on me but it means whoever is providing my internet won't know I'm using Twitter or be able to identify me based on the outlinks I follow.