Well, I agree about the cost, but I am not 100% sure that you need to put all your home directory in an external drive. It is easier (or better) to have the home directory in the internal drive, but keep the larger data in an external drive. Usually just two directories, Desktop and Documents are connected to the iCloud, and you don't have to keep larger data is either of them. The Desktop is for the work duration, and the Documents can keep symlinks, if there are larger files/folders somewhere else. iCloud is quite a useful thing, by the way :)
Maybe, it is the quality of your external disk, or the connection cable to the Mac Mini, or even the connection slot. Just check whether you can keep your Home directory, even a slimmed down one, in the internal disk.