Moving from Google (Android) to iPhone I have been using Android for many years, now I have an iPhone.

I am used to Gmail, having my Contacts as Gmail contacts, Google maps, backup of SMS to Google, Chrome with sync of online bookmarks, backup of photos to Google Photos, Google Calendar (in browser)

Basically, in what cases should I look for "native" replacements, and in what cases is it natural to use Google stuff?

(I have used the migration app)
To start, congratulations on the upgrade :)

Now, what I would do is connect the old phone to my computer (Mac or PC), open Finder (or My Computer), and double-click on the GUI representation of the phone to see the contents, now take the folder marked "DCIM" and copy to your computer.

If you have a Mac, open Photos (10.10.3 or later, for earlier see the Windows method below as it's about the same). Now, import the folder into your photo library and sync the library to your iPhone.

On Windows, you'll need to download iTunes from Apple (nowhere else) and then follow this Apple support article, scroll down to "Sync your photos manually with iTunes."