I will argue that a properly secured and backed up computer connected to the cloud is safer than a single PC that is never connected to the internet and backed up to storage and I'll explain why.

If you have a stand-alone computer that you back up regularly (every time you use it would be ideal) you then have two copies of your data.  You then need to take one of those copies offsite and place it in secure storage.  A fire rated safe will not guarantee its safety.  Storing it in a safe in your shop 100 yards from the house is better but you still only have two copies and they are within close proximity  of each other.  The same event could render both of them useless or lost.

An internet connected computer that is configured to automatically back itself up to a cloud based service means you have the original copy on your PC and then multiple copies stored across the globe.  If done correctly with a reputable service (who can verifies its encryption with a third party) gives you redundancy.

Personally, I store my data on cloud based service (Google Drive, Microsoft OneDrive, DropBox) and then have a Network Attached Storage device that I have located in the concrete storm shelter in my basement.  It has a fire rated door and the device is located 20' away from the door.  The NAS actually backs up my cloud storage accounts to itself so I have multiple copies on my devices as well as cloud backup.  I also create image backups of my PCs that are stored on my NAS.

Lance highlighted the most important part about internet safety.  Don't click on links you don't trust.  Don't visit questionable sites.  Hackers are not going to spend the time to try and brute force their way into your network when it's much easier to have you open the door and let them in.