Here's one way:
All local users are members of the plugdev group by default in Ubuntu.
sudo chown :plugdev /home/share
The "2" makes it so every new folder / file "inherits the group.
sudo chmod 2775 /home/share
The "7"'s make sure the group has add / delete access to the share.
But there's one more thing necessary to pull this off:
Edit /etc/profile as root:
Find the line at the bottom that references umask and change it to:
gksu gedit /etc/profile
What this will do is change the permissions on newly created folder / files from 755 / 644 to 775 / 664. Now memebers of the group can write to the file.
You will need to logout and log back in again since profile is read only once at login.