Turning on iCloud syncing will work for everything at once-- turn them both on! Just to be clear, iCloud Photos is a synchronization service. When you engage iCloud Photos on a device, then the Library on that device is kept just the same as the iCloud Photos Library. So, for instance, if you take a picture with your iPhone, it is added to the iPhone's Photos Library, copied to iCloud Photos Library, and then copied to the Photos Library on each of the other devices that you have connected. If you delete a picture on your Mac, then that picture is deleted at iCloud and on all the other devices.
So, the whole point of iCloud Photos is to have it connected to multiple devices. You do need to be sure you have room on both your devices and at iCloud.com. The free 5GB, for instance, would be good for only a few hundred pictures.
iCloud Backup is entirely separate and, if iCloud Photos is turned on, then Photos is not included in the backup--that would be doubling the storage.
iCloud Photos syncing is a sort of backup, but only partly. If your Mac gets run over by a truck, then your pictures will still be available through iCloud Photos. But if you accidentally delete the pictures of your sister's wedding, don't expect to go to iCloud and get them back-- they were erased there, too. iCloud Drive is a synchronization service, not an offline storage or backup service. If you don't have a Mac, then the best practice is to periodically copy everything to a hard drive for a real backup.
