These instructions are if you want to be connected to the internet but still pretty private. For an offline iPhone (more private, but syncing with the computer has to be done manually), alternate instructions are here.
Although I definitely do not recommend buying an iPhone, sometimes we get stuck with them. Especially if you try to always buy used phones, which is a good idea. A phone with LineageOS and without installing the Google apps is a much better choice for a privacy phone that gives you choices, and this is a good guide for better privacy, but if that involves buying a new phone from Amazon as opposed to making do with an old phone that nobody wants, then some of us are stuck with an iPhone. Apple probably tracks you less than Google, because tracking is Google's main business model, whereas Apple's business model is to try to force you to use Apple services and buy more Apple products.
So the idea here is using an iPhone minimally, as just a phone plus any offline apps you find useful (Camera, alarm clock, etc.). It's less convenient and you have to jump through a ton of hoops because of Apple's limitations, and I can't guarantee it will work, but in the end I was able to get a more private iPhone 8 than I would have by doing things their way.
When you set up the phone for the first time or after a factory reset, don't create an Apple ID and don't get an iCloud account. The interface makes it non-obvious to avoid creating one but it should be possible, at least on the older models.
To sync your files, calendar and contacts with your Linux computer, install a Nextcloud server (self-hosted) on your Linux computer, as well as the Nextcloud client on the computer, and the Nextcloud iOS app on your phone. Instructions to install the server are here. With iOS, you need to set up SSL, and since the files will be only made available on your home network, it has to be a self-signed SSL certificate, as described in those instructions.
An advantage of using the Nextcloud app on iPhone is that it lets you edit your text files on the phone, which the iOS Files app doesn't allow, and it's difficult to find a tracking-free app that allows you to do that. The Nextcloud app is listed in the App Store as doing no tracking (and is available on F-Droid too for Android devices).
It also has the option to copy pictures you take to Nextcloud, so they can by synced.
However, Nextcloud still has severe limitations. The files still can't be edited on the phone when offline, and even when online, it's very slow to load the editor. Also, if you try to access the files when online but when your Nextcloud server is down (e.g. if your computer with the server is turned off), you get an error. So this isn't a backup. As a result, it may still not be worth syncing files via Nextcloud. Could just sync calendar, contacts and photos, and use these instructions to sync files manually via USB cable.
Note: For music, I copied my music to my phone once via iTunes in Windows, then don't need to sync it anymore. Perhaps a Nextcloud music app would be a better solution.
For web browsing, there's no good option. Unfortunately Apple forces you to use Safari - other browsers on iOS are just "skins" for Safari. The important thing is to get into the habit of not surfing the internet on your phone. Wait until you're at your computer, although there are some sites which don't track you which are pretty safe to read on your phone, such as this one. This may seem like a big limitation, but web browsing on a phone is slow anyway, so getting into the habit of going to your computer to search something can be beneficial anyway.
So as you can see this process will not fully protect you. To be 100% protected you have to live without a cell phone. But it's a compromise that minimizes, rather than eliminates, Surveillance Capitalism.