Sharing a directory across multiple server accounts

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I'm trying to share a directory with multiple accounts (all owned by me; in  
fact, every account on the server belongs to me). So,


should be able to be modified by both user "example" and user "new".  

Here's what I've done:

# Add "new_username" to group "example"  
#   Note: the -a here is for "append", so new_username can modify files  
#   under both groups "example" and "new"  
usermod -aG example new_username

# Change permissions for each directory to be shared  
umask 002
chmod -R 2777 /home/example/images/

But I still get "permission denied" errors when I try to upload from /new/.

My server provider suggested that I chown the entire /home/example/ directory,  
as well as every subdirectory that I would like to share, like so:  

chown /home/example/
chown /home/example/www/
chown /home/example/www/images/

When I did this to a test directory, though, it showed the Owner/Group as:  


Now, since I added "new" to the "example" group earlier, this looks backwards  
to me. Why am I changing the group to new? Would making this change leave  
"example" unable to make changes to its own directory, since they now belong to  
a group that "example" doesn't belong to?

/example/ is a very active account (my bread and butter), so I really don't  
like doing anything to it that could mess it up. So before I go and make a mess  
of things, I'm hoping you guys can confirm... is this right?

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