I think you need to first clarify what your situation is. Are you using iCloud Photo Library or not?
If you're using iCloud Photo Library, if you delete a photo from your iPhone it deletes it from iCloud too (and any other device connected to your iCloud Photo Library). The solution here is to buy more iCloud storage, or accept that you need to start deleting photos from iCloud to stay under your current capacity limit, whatever it is currently.
If you're not using iCloud Photo Library, then you have Photo Stream and Camera Roll on your iPhone. As I mentioned above, Photo Stream does not count against iCloud storage, but your device backup does -- and if you have a large Camera Roll, and thus a large backup, then that can create a capacity issue for iCloud. The solution here is to either backup to your computer (via iTunes) instead of iCloud, and/or copy photos from your Camera Roll to your computer and then delete from Camera Roll (a good idea anyway -- people tend to carry WAY too much in Camera Roll).