Have members with 'Read only' access

[kelsey0]

We set up a SharePoint intranet for our company. There are the 3 SharePoint default groups under site permissions (1 group in each: site owners, members & visitors), but if I add a person to one group they're added to all 3 groups. This gives them all access. We want staff to be members so they are able to use applications in SharePoint (example: Planner) but we do not want them to be able to edit the intranet. They are unable to view the applications if they are visitors/'read only'. This is a private teams SharePoint. 

Things I have tried:

1. Adding staff to the default site visitor group (read only) and wanting to remove the group from 'site owners'.

Outcome: There is no option to remove the group from 'site owners'. The group will continue to have owner abilities.

2. Creating a new group through 'Advanced permissions settings' to be assigned as 'read only' and adding in staff.

Outcome: I am able to create the group and add staff. This group is not visible when clicking on Gear>Site Permissions. Is there a way I could add this group to the site permissions section?

Are there any other suggestions on how I could resolve this issue?

Thank you in advance!

[#2]

Update:

My solution for this is for situation #2.

I had created a new member group and added members to it. Then I had to add them to the Site Visitors list through the Advanced Permission Settings (seen in attached). This group now displays under Site Permissions>Visitors. They seem to be members with 'read only' access. This is how to add members as read only. They are still unable to view the Planner application.

This application has its own group, which is different from member groups on the Site itself. Members need to be added to their specific Planners as well through the Planner application. I believe this can be done through the Outlook Planner interface. I have been instructed that we no longer need the Planner application so I will not be pursuing the issue any further but that's what I got from my experience.