Do I need to pay for iCloud storage and Google photo storage on iPhone?

Your needs will depend on the apps that you are using and where you want to store your data. iCloud storage is used for the native cloud backup of your iPhone as well as things like storing your Photos, Messages, and data from other native apps in the cloud. Apple gives you a free 5GB of data in iCloud that is suitable for very minimal use such as keeping your iPhone backed up. If, however, you will be enabling iCloud Photos you will undoubtedly need to purchase more iCloud storage. If you plan on staying within the Apple ecosystem (i.e. iPhone, iPad, macOS) then iCloud is the way to go.

If, however, you plan on continuing to use apps provided by Google because you are invested in that platform, then there may be no need for you to purchase additional iCloud storage from Apple. Instead, you would just keep subscribing to your Google cloud storage account.