If you're wanting to use disc based archiving, use Millenniata M-Disc. Verbatim also their own M-Disc.
Verbatim claims: Based on ISO/IEC 16963 testing, M DISC media has a projected lifetime of several hundred years.
Millenniata claims: Properly stored M-DISC recordings will last 1000 years.
How to property store M-Discs
The M-DISCâ„¢ is extremely durable and does not corrupt even in extreme environmental conditions (heat, humidity, light, etc.). However, we suggest storing M-DISCâ„¢ products upright in plastic or steel containers manufactured specifically for the type of medium in cool, dry storage that is free of large temperature fluctuations.
Concerns
Despite the base of their claims, it still does not absolutely guarantee no data loss. You're backing up your media one time on a disc. You don't have redundant copies in case something does go wrong with one. In the event you make multiple copies of a disc, they are still in the same geographic location. If something extremely tragic happens, for example a house fire, tornado, house robbed, etc, you could lose all of your data.
If you make extra copies to give to people you have to worry about them keeping it safe. They could lose it, damage it, throw it out, or have an extremely tragic event themselves. It's also driving up the expense of material and time you spend archiving the data.
My opinion on the cloud
Storing them in the cloud is the safest way. You don't have to worry about depending on them at all. They have more reliable up-time than your own ISP. They have your data backed up and archived way more than you're aware of. Their data centers are copied and stored at several sites, in vastly different geographic locations. Having it online also allows you to easily browse and look at your photos too. You have much more sensitive data that could lead to identity theft and other large problems, stored on a server somewhere. Storing personal photos online would be one of the least concerns to me.