I don't think it's really feasible to back up a large library to the Cloud unless you have a enormous bandwidth. I would make two suggestions to your back up routine:
1. You need an off-site back up.
2. Back up your Photos to the cloud, not your Library.
My Library lives on my iMac. It’s Backed up to two external hard disks every day. These disks are permanently attached to the iMac. These back ups run automatically. One is done by Time Machine, one is a bootable back up done by SuperDuper
It’s also backed up to a portable hard disk when ever new photos are added. This hard disk lives in my car. For security, this disk is password protected.
I have a second off-site back up at a relative’s house across town. That’s updated every 3 or 4 months.
My Photos are backed up online. There are many options: Flickr, Picasa, SmugMug etc. However, check the terms of your account carefully. While most sites have free uploading, you will often find that these uploads are limited in terms of the file size or the bandwidth you can use per month. For access that allows you to upload full size pics with no restrictions you may need to pay.
Every couple of months I test the back ups to make sure they are working correctly. It’s very easy to mis-configure a back up application, and the only way to protect against that is to do a trial restore.