“secure” is a relative term, so it’s really hard to give you a definitive answer for that.
That said, I feel that the “security” option does a good job of “protecting” your data from other users on the server, and from the public.
As for “anything else you need to do”, I think that all depends on the nature of your data/files. The directory is pretty secure as it is, but this is someone else’s server (DreamHost’s), so you need to recognize that system backups will contain your files, and all files on the server are accessible by the root user (DH Admin). Therefore, if your data privacy is critical, you should either not put it on the server at all, or encrypt it.