I am not sure I should take this on but I will give my best. @Alexis or @Kaitie_Saballus or @Todd_Cavanaugh or @paulminors may be a better source but here goes.
There are some varibles that depend if you have a paid or free subscription.
Teams: If you are setting up a new Team, the free version will always require membership by request whereas the paid has the option of membership by request, hidden or public. Be conscious of what you want seen by the whole organization and outsidrs.
Projects: THE STATUS of THE PROJECT IS CRITICAL. The free account only allows Public to the Team or Private To Me, whereas the paid account allows Public to the Team or Private To the Members. With this in mind take a look at the (4) links that I have provided below to get a feel of what can be seen and how you would set up your defaults on Team and Projects depending if you use the Paid or Free Version.
I deleted my previous long winded post and put a short reply last.