group with default permissions

is there a way to change the permissions of "Members"?  Created a permissions level of "restricted user" which is all permissions of the basic member but takes out the ability to delete a file.  Otherwise I have to use a new group that allows me to change permissions for the group to this new level.  But then how do I get them to show as a "member" to the site?  

Perhaps this can better be explained.... 

Library: Working Files

In that library, there are separate folders and under each folder there are files saved

I.E. Folder: Production

File 1: 1st Shift

File 2: 2nd Shift

Folder: Materials

File1: Shipping

File2: Drivers

So what I need is for some users to be able to access 1st shift but not 2nd Shift and perhaps a user needs to access 1stShift under production and Shipping under materials.  

Therefore, was adding people to the group "users" then after they were added, I would go to manage access for the specific folder / file and add them (the user).  The problem is that while the group "users" is "restricted access", the user is showing permissions as "contributor".

Not too many users will have the same exact access to same folders / files.