Setting up a virtual host on LAMP (Ubuntu 11) returns 403

If you're having trouble changing the group on the folder, make sure that you're root. You can't change the group of a folder or file unless you are the owner and in the group, or you're the superuser.

Ditch the admin GUI and open a shell. (Terminal, xterm, etc.)

chgrp www-data /home/morpheous/work/websites/testproject
chmod 2770 /home/morpheous/work/websites/testproject

# Set mode rwxrws--- the '2' sets the 's' sticky bit,
# which causes all files and folders created in "project"
# to inherit the same group.

(This may not be the best way to configure this specific app, but I think it's a reasonable guess. I'd also recommend moving that out of your home directory... that just complicates trying to keep your personal home directory secure while giving the webserver access to write to part of it.)

As for keeping Apache from serving up files in those directories, that's already done... your document root is defined as project/web. That only gives access to files at that point and below... the log and cache folders are already excluded.

It looks to me like a simple permissions issue. On Ubuntu Apache runs as user www-data group www-data. As we can see from your directory listing the permissions on your ~/Dropbox directory (via .) are drwx------ or 700. Thus Apache as www-data:www-data is denied access.

chmod 755 ~/Dropbox

will probably fix the immediate problem. In general you will need to provide o:rx permissions on directories and o:r permissions on files to allow Apache to access the files.