It is dangerous to place live files on your backup disk. If and when that disk crashes you will lose those live files. They need to be backed up on a separate backup disk.
Purchase two hard drives: one for Time Machine and one for to offload your live files. The Time Machine drive should be larger than your offload disk plus your system disk because Time Machine is going to backup both of them.
Format the drives as Mac OS Extended (journaled) and plug them in.
Then > System Preferences > Time Machine > Options… > Remove the offload HD name from the exclusions list.
Now both your system disk and your external offload disk will be backed up onto your Time Machine disk.
For more about backups:
Time Machine Basics: http://support.apple.com/kb/ht1427
Most commonly used backup methods:
Methodology to protect your data. Backups vs. Archives. Long-term data protection:
PlotinusVeritas gives some great suggestions for purchasing external hard drives in this thread: