Here's the easiest way to make the jump from Google Photos to iCloud Photos. Each iCloud account comes with 5GB of free storage, after that you'll need to sign up for a paid storage plan that ranges from $0.99 for 50GB to $9.99 for 2TB. Keep in mind, Apple doesn't offer free photo storage. Instead, you'll have to complete the process on your own, which will take a few days from the time you request a complete copy of your Google Photos library until you've successfully uploaded everything to Apple's servers. If Google's switcheroo has persuaded you to make the jump to Apple's iCloud Photos service, you should know that there's currently not an official Google feature to transfer your library to iCloud. It keeps your photos synced between all of your Apple devices, you can search for objects in the photo - including a specific person - and better yet, it does all of the advanced stuff on your device, keeping your photos private.
As an iPhone user, the built-in Photos app offers a lot of the same features as Google Photos.