iOS has reasonably good default privacy protections, in Safari and for apps, and they get better with each release. There are settings you can lock down further. However, those doing the tracking are always working on better ways to track you too. You definitely do not want to allow apps access to sensitive data like Location, Photos, Contacts, Calendars, Local Network, Health, Camera, etc. - just say "No" to pretty much every dialog that pops up asking for permission to access something. Also, turn OFF "Background App Refresh" so that apps can only phone home when you open them.
In general, a Private Tab in Safari will be better than an installed app. There are some caveats, like if you have a consistent IP address. You can turn on "Hide IP address" in Safari Privacy Preferences to help with this.
Other than logging in and identifying yourself to the service (and therefore providing a wealth of information to that service), the biggest challenge for avoiding tracking in web browsers and apps is device fingerprinting. This is somewhat outdated, but there's a history of discussion of this topic here, and elsewhere.
There are other strategies to help protect your privacy, that you can use in conjunction with locking down settings: don't log in to a service unless it's absolutely necessary to accomplish the task at hand, create accounts with pseudonyms, use separate email addresses and phone numbers or other required contact info for each account, minimize the amount of personal information you share (you can often leave fields blank), and supply misinformation wherever possible (keep it legal). Strongly consider using alternate services that respect your privacy. There are no absolutes in privacy or security, always trade-offs that depend on your priorities. But every little thing you do to strengthen your privacy is a win.