Here is my suggestion. It may be overkill for you but I do this. First, off get a second internal drive for backup use that has enough room for all that you need. Partition it in a way that suits your backup style. Personally I just go with one main partition, but I understand your need to limit your backup software. Once you've done all your backups as needed and have everything in place, take your external and make a copy of your internet backup drive.
There is a method to my madness, and these are lessons i've learned over the years :
1. You should always maintain proper backups, and that includes redundancy of the backup itself.
2. Internal drives make better backup drives because they are more accessable during every day use (they don't require power-up) and you benefit from full SATA speed. Obviously "better" or "worse" is a matter of opinion, so take it as such.
3. Offloading backup duties from your system drive will provide more room to breath as well as making a system crash much easier to bounce back from (assuming you have a proper image on another drive).
4. In my experience, external drives tend to fail more often than internals due to the additional interface circuitry (more parts to fail) , and thus IMO shouldn't be used as a primary backup device. This is especially true if you plan to backup often, or plan to keep the drive running all the time, since wear and tear can reduce external life considerably. This is another reason why I prefer internal drives for primary backup.
Obviously this is just one way of doing it, and doing a single backup to external will work fine for most people. Personally, I assume all hardware eventually fails and plan accordingly.