I got it. It is more complex then I initially thought. But, if someone needs to really quickly adjust menu links to be hidden for certain groups - here's the way to do it. (This is definitely not the correct way but "lazy/easy" way):

1. Create your Group
2. Assign Admin rights (same as Admin group) to the group
3. Find User Interface -> Menu items you need for group and set your group to it with admin group.
4. Repeat 3. for all links you need.

I repeat, this is not the right way (I'm still learning the proper way to configure user rights), but I hate leaving my questions unanswered.