No longer storing photos on iCloud

"I currently have an iPhone 8 Plus which some of the photos of my phone are stored on the phone (256gb) and some on iCloud."

If you are using iCloud to store your photos, then all of your photos are stored in iCloud and also on the device as well. That's how iCloud works.

How do I stop storing the photos on my phone on iCloud?

You cannot when using iCloud. iCloud works by storing your data in the cloud whilst also storing a smaller footprint of the data on your device.

If I turn off iCloud will it delete my photo's stored through iCloud?

Yes.

Or will all my photo's still be on my phone and then I can do a computer back-up before transferring to the new phone?

No, it'll be both on the device and in iCloud (see what I said above).