What data is best for the cloud? This might seem a trite question, but storage is evolving very rapidly today. We have speed changes that are amazing, with performance from SSD and flash cards hundreds of times that of hard drives, new ways to store, new cost models, and new places to store data away on both short- and long-term bases.
For the committed SaaS user, this is a different dilemma than the general IT question. If you've committed to SaaS, you've also committed to letting some of your data go out of your control to a remote third-party. Typically, you are managing that data indirectly, using the SaaS shop to control it for you.
What about all the rest of the data? First, all the data on your file servers is worth looking at more closely. Most of the data is at rest most of the time, and if file servers weren't cheap, they would have been shoved onto a tape and parked away long ago. In fact, one of the problems with your file servers is that they are cluttered with evolved copies of old files, names tend to be reused, and figuring out what is most useful requires a discipline that just doesn't exist.
Worse, backups are often a bit hit or miss. In other words, file servers are easy to use, but tough to use well. Consider moving old data to the cloud. It gets de-duplicated, compressed, and encrypted, and it's automatically replicated for protection. This used to be very manual as a process (a year ago), but a new class of storage appliances, the Cloud Gateway, is making this a simpler transition. In fact, it is possible to add the gateway software to an existing box, saving money. The neat thing is these gateways provide a NAS function, with a hybrid local and cloud storage, and tier useful data to the local storage, where access will be as fast as the original file server.
Touching on backups, the gateways usually can act as a backup device for all the desktops in your network, and because the backup is to a remote site, you have a disaster recovery package, too. Overall, the idea of moving to a hybrid cloud gateway structure simplifies management and will lower costs over time.
CAD and other design data need similar treatment. Here, the amount of storage is usually quite large, since CAD files are big. It's crucial to organizational existence that this data is always backed up, and often, the ability to roll back to an earlier snapshot of a file is important. The cloud is again a good place to store the snapshots. Some of the gateways explicitly support snapshot activity, and with others an end-of-day or background backup would be enough.
It wouldn't do to use the cloud as the primary storage, and the applications for CAD run on powerful local workstation, so a gateway with a lot of local storage is needed. Check that the box can be expanded to hold enough capacity, and consider using SSD or even a flash accelerator drive for the local capacity, to reduce latency and load times.
Databases are a different class of issue. Because response time is a crucial benchmark of usability, going to the cloud for data is a non-starter with today's slow WAN links. This would change with fiber-to-the-premises systems, and some countries are heading that way rapidly, but not the US.
For the moment, databases would be best served by local fast storage, and ideally SSD or PCIe flash cards. Inactive, older data could be moved off to the cloud, though, saving the space on those expensive, enterprise-class SSD drives.
Finally, the websites for the company really belong in the cloud. Both compute and storage could go there, and be run efficiently, without requiring expensive, local data links. In this situation, data could be either in object storage, or in a block storage service, and the determining factor is the topology of the vendors' services (they may prefer block for their compute service, for example) or the cost profiles involved.
The rationale for the cloud is that compute needs are very variable, and the on-demand nature of the cloud gives the best overall usage/cost profile. You have to do the sums, but I think this is mostly true.
Hopefully, this has given a clearer insight into the cloud opportunity. Issues like security and availability are reasonably well understood, so most of the question comes down to the price and any performance hits involved.