Can I have My Photo Stream upload only?
What you want to do is enable iCloud Photo Library on all devices, and then disable photo stream (or at least optimise storage) on your mobile devices. iCloud Photo Library is the actual cloud storage, while Photo Stream is just syncing between your devices (and not the cloud).

Note that Photo Stream only keeps your last 1000 items downloaded on a device. Photo Stream provides no backup if you lose all devices at the same time (if you carry them all with you and something happens).