Disc media, e.g. DVDs, are not necessarily as reliable as people may think. Your time machine is actually already a very good solution. The likelihood that both your hard drive and your time machine would fail at the same time is low, and one can be used to restore the other. The only thing that might improve your backup is adding off-site backup; for that, you could add backup to a cloud service.
With regards to a cloud service, you need not choose a service that is explicitly about backup either. It could be a service that is aimed at media sharing (photo + video), and in this way you could use the service as not only a means of backup, but also for sharing those photos and videos with friends and family.
It sounds to me like you haven't identified a business need and are fishing for one. Wouldn't it be better to look at how the business operates and from there see if there is something that can be done more efficiently? If there is, then ask yourself how this server can be used to address that problem. A server can do a lot of things, but don't look at those things and try to force it on the business when the need doesn't necessarily exist. It may create more problems then it solves.
If what you are really looking for is something to play with, then Filemaker sounds like a great place to start. It could be your introduction to databases. Once you understand the power of databases, you may find areas of the business that might benefit from a database. But until you have the knowledge, you aren't in a position to implement and support one. Just remember, if you're going to play with something, don't do it on a production server. Backups are a real business need. Even if that is the only thing the box is used for, it is a perfectly good reason for its existence.
"The one charm of marriage is that it makes a life of deception a neccessity." - Oscar Wilde