What do Ivy League schools look for in academic honors?

I’m having trouble deciding which 5 honors and additional academic information I should supply in my applications. Do Ivy League schools (specifically Princeton, as it is my college of choice should I be accepted) take all things into account for academics? For example, Im 4th in my class, and don’t have a 4.0 (my unweighted is about a 3.87, weighted is 4.195), but the valedictorian of my class, the class above mine, the class above that one, and the class below mine (I could go on) do/did not not have 4.0s, as far as I know no one has ever gotten a perfect 4.0 GPA. Will Princeton recognize this when they see my transcript? Or will my imperfect GPA be a large detriment to my application?

Also, I just achieved the AP Scholar award, should I include this in my academic honors? I took AP Art History as a sophomore, and as a junior took AP US History and AP Physics, and received scores of 5, 5, and 4, respectively. My school only offers 8 AP classes, and two of those being foreign languages, it is impossible to take both AP Spanish and AP German because of how the scheduling works out. So again, will Princeton look down upon my course schedule, since they will see out of 8 possible APs I took 7? And will they still value the AP Scholar award, despite its lack of distinctions (the only way for me to get distinctions would been to take classes on my own which I did not due for fear of hurting my required school work)?

In the “additional information” section of the application I planned on adding the fact I took the most rigorous course load possible at my high school, but should I include the fact its only possible to take 7/8 APs or the fact that a perfect 4.0 at my school is to my knowledge unachievable?

To go along with my original question, I have all 5 slots for academic honors filled. The 5 are honor roll, NHS, WBL All Academic Team, National Merit Scholar Semi-Finalist, and AP Scholar. Is honor roll a valued honor, and is NHS worth putting? WBL All Academic Team is for receiving above a 3.5 and at least 2 Varsity Letters in sports (does not include band or Quizbowl), so would I explain this in the additional info section as well?

Your school will be asked to indicate your class rank (if available) and whether you took the most rigorous possible class schedule. If a 3.87 puts you at or near the top of your class and you’ve taken what you can, this will be sufficient for this part of the application.

International Honors > National Honors > State Honors > Regional Honors > School Honors

The Counselor can mark ‘Most Rigorous Schedule’ so there is no need for you to do so in the Add’l info section. The school profile will also be included so that College can judge you against your peers.

It’s not a problem that you don’t a have a perfect GPA. And taking ever AP offered by your school except one is very good.

As to the original question, I don’t think it will matter much which Honors you list.

Good luck!