The naming of the parts
Assembling the parts named
It is a very useful exercise to develop your own Library structure 😉 . The second link above details many of my thoughts while I was first putting together Aperture 3 Libraries.
As Léonie has already indicated, your first mapping is commonly proposed, and inverted. Until you are completely adept with Aperture, stick to "one Project = one out-in-the-world shoot". This is how Aperture was designed to work (afaict) -- starting off that way will give you the broadest geography you can cover without crashing into an unanticipated fold in the landscape.
I found it very helpful to understand and utilize the fact that I use the Library for two distinct tasks: storage, and retrieval. (I use the program for Image development, but that is in effect independent of the Library organization.) My solution is to separate these structures, with Projects (organized with Folders) as a filing system for all my Images organized by "shoot", and Albums (organized with Folders) as a filing system for all of my output projects (small "p" projects".
This works well for me, partly because I am a fine art photographer, and my projects (again, small "p") almost always span several shoots. For instance I am preparing an entry for a show of small works on paper. I have created a Folder for this, in which I put an Album holding the 100 or so Images I'm considering entering. These 100 come from at least 30 separate shoots. I will whittle this down to four, mark them as the ones I entered, and leave the Folder in which I can always see which Images I considered, and which ones I selected.
What works for me is unlikely to work for you -- but it should give you some surveyor's marks as you plot and dig your own Library foundation.
Read the linked messages, play around a bit, and post more. There are very few needs that Aperture can't meet.