How can I use an existing Apple ID on a new iPhone, WITHOUT transferring all my images?

You do not have to create a new ID. When you activate the new phone, just don't restore the backup of the iPad or don't download your purchased content to the device. You can go to Settings>iCloud>Photos>My Photo Stream>Off and any photos that you take with the phone will not transfer to the iPad. Do the same thing on the iPad so that photos that you take on the iPad don't appear on the phone.

In a worst case scenario, you can delete any content that would download to the phone. When you log into iCloud on the phone you will have to turn iCloud Photo Library on before it would start downloading. It should be off by default as long as you DO NOT restore the phone from the iPad backup.

I Don't understand your remark about having to need more storage if you turn off Photo Stream. That doesn't make sense to me.

Hawkmz wrote:

Can it be ON on my ipad, and OFF on my iPhone, and the images wont transfer in any way?

Yes. The photos will not disappear unless you delete them from iCloud. You can use iCloud Photo Library and not use it on the phone and you will not lose the photos. They will not transfer to the phone if iCPL is off.

However, you should never, ever rely on cloud storage only as the only way to save your photos. Even Apple (as much as they want you to keep buying more storage) tells you to download the photos to a computer for a REAL backup.

It would not be a bad idea for you to read this.

iCloud Photo Library - Apple Support

When you turn on iCloud Photo Library, your photos and videos automatically upload to iCloud. They're not duplicated in your iCloud backup. But we always recommend that you keep back up copies of your library. You can download your photos and videos from iCloud.com to your computer and store them as a separate library, transfer them to another computer with Image Capture or Photos, or store them on a separate drive.

https://www.quora.com/How-do-I-stop-iCloud-from-syncing-everything-to-everything

IF you are using iCloud Photo libraray on the iPad, then the photos will appear on the phone. You can turn that off on the phone. Just do not use iCloud Photo Library on the phone.

As long as you do not restore a backup, you will be starting with a "clean" phone, as you have called it.

You will have to turn it off on the iPhone once signed in and then in your setting go to the iCloud options and just turn off the photos. and doing so will keep your phone from receiving any of the iPad info

You are quite welcome. Good luck with your new phone. Enjoy. 🙂