Depends how paranoid you are, what services you use, and what information you're fine with them having.
If you have google play services installed, it won't really make a difference if you use the play store or any google apps, they already have full access to your device.
If you're using a ROM without google play services or any google apps installed, then Google will have a harder time getting any useful info from you.
However, many apps will use google analytics, firebase, or another google service within the app itself, so its very unlikely you'll be able to completely prevent google from obtaining some limited information about your device/app usage.
Signing in to google within a browser could allow google to link your account with that web browser's fingerprint, so if you visit any sites with Google analytics or other google services, google could determine what sites you've been visiting.
Your best option is probably to use some FOSS apps for whatever google service you're using in the browser.
Or, use those web services in a separate browser to the one you use for everything else.