How to partition External HD for both Time Machine and other purposes?
You can make the partitions any size you want. The larger you make it, the more backups you can save. TM deletes the oldest backups when it needs more space. You can also define what you backup in TM options. I don't like the methodology, but it takes the approach to back up everything. 

You have to exclude things for which you don't need backups. For example, you may not want to back up the System itself. You may not want to backup some apps - where you can reload the installers. 

Basically, you want to backup only stuff that you don't want to lose. So documents, images, music, work, etc.

If you have a 100GB of that stuff, you may want to make a 200GB partition. Then, other than a full backup of this data, TM has 100GB to make incremental backups of things you create or change.

I hope this helps. From your question, it appears that you know how to partition the disk so I did not go into that. Let us know if you need more on that.