Once I've ssh'd into my remote server, what would the command be to copy all files from a directory to a local directory on my machine?
From your local machine:
rsync -chavzP --stats [email protected]:/path/to/copy /path/to/local/storage
From your local machine with a non standard ssh port:
rsync -chavzP -e "ssh -p $portNumber" [email protected]:/path/to/copy /local/path
Or from the remote host, assuming you really want to work this way and your local machine is listening on SSH:
rsync -chavzP --stats /path/to/copy [email protected]:/path/to/local/storage
See man rsync
for an explanation of my usual switches.