You have come to GeoNet for one main reason ... to get an answer, but you wonder where you are supposed to post your question. What is the difference between In a Place, Specific People, and The GeoNet Community? Right off it seems The GeoNet Community would make your content get the greatest exposure; however, that is not necessarily the case. Below I break down each option to help you get the best audience.
In a Place
In a Place allows you to select a space or group (see What are Places? for the difference between the two). You can enter the place name or browse for places directly from the dialog. The formal space structure can be seen in the GeoNet Community Structure document, or you can review the ArcGIS Discussion Forums Migration Strategy document that provide an overview of how the ArcGIS Forums were aligned with GeoNet spaces. You can also search spaces and groups from the Places Tab.
When you select a place, anyone that is following that place will be notified of new activity when you post your discussion. This allows those the have a specific interest to see your discussion and provide an answer. The content also shows up in the activity stream of that place for others who are may be browsing the place to see it.
Also be aware that content posted to secret and private groups you belong to will only be visible to members of that group.
Specific People allows you to create a private discussion between specific GeoNet members. Other GeoNet members will not see the content, and it will not show up in other member's searches. You or others in the conversation can later add people to it.
The GeoNet Community
The GeoNet Community allow you discussion to be visible to everyone within the community. The content will be visible on the home page activity stream, and within your own personal activity stream. The discussion can be found through the search, unless someone looks in specific places within GeoNet then it will not show. This is the broadest net to throw, but keep in mind that it's part of a very large crowd instead of the targeted places or people.