Normally, you want you Lightroom catalog file on your fastest disk, unless you have some other over-riding reason for putting it elsewhere.
Normally, with Lightroom, you don't save a copy of your final edited images on your hard disks, as the final edited image can always be displayed and created by Lightroom; in other words, your exported final images are considered temporary, and deleted once their use is completed (e-mail, web, print, etc.) knowing you can re-create them again exactly as before by exporting another copy.
Your original photos can go on any online disk you want.
Backups of original photos and backups of your catalog file can go on any disk you want, online or offline.