Since you have general questions, you will do much better starting with a guidebook (or several) than a travel forum. I'd start by hitting the library, and getting as many as they have. I'd definitely buy Rick Steves Paris (the 2016 edition is already out); he has the best logistical help (exactly where to catch a bus, for instance). But he only covers what he considers the highlights, so you want to look at other books too.
If you prefer watching to reading, here is a link to Rick's TV shows; click "France" and you'll see he has three on Paris, from 2012 and 2014: http://www.ricksteves.com/watch-read-listen/video/tv-show
There is a Paris Museum Pass, a Paris Visite Pass, and a Paris Pass. They are three different things, and yes it is confusing. The Paris Museum Pass can be a good deal for many people (you should still do the math to make sure it meets your needs); the other two are bad deals for most people.
The Museum Pass allows you to skip ticket buyer lines (only an issue at a few places, including Versailles, the Louvre, and the Musee D'Orsay). But it does not allow you to skip security lines. If you're not getting a Museum Pass, you can buy advance tickets online for individual places through their websites and skip the lines that way.
The Museum Pass and what's covered: http://en.parismuseumpass.com/rub-m-by-name-5.htm
For transit, there is a Pass Navigo, good for unlimited bus and metro use in Paris from Monday through Sunday. If most of your visit coincides with this, it's a great deal. If not (for instance, if you're there Wednesday through the following Thursday), just get carnets - sets of 10 metro/bus tickets, for the price of about 8. These are shareable and never expire. Many people end up walking around Paris more, and using transit less, than they expected.
If you know when you want to go up in the Eiffel Tower, you can prebook. But the tickets disappear within minutes of being released, so many end up either booking a tour, walking up partway (much shorter lines than for the elevator), going in the evening (often shorter lines), waiting in the long line, or not going up at all and just seeing the Tower from great vantage points like the Trocadero and the top of the Arc de Triomphe.
Of the many famous sights, I love Ste-Chappelle. The museum pass does not get you past security lines, and this one is often slow because the chapel is in the same complex as a criminal courts building. So, go first thing during the day. It's worth skipping breakfast to see Ste-Chappelle early, before it gets filled up.
What to see will depend on your interests (the reason to start with a guidebook). You don't have to go anywhere, so don't feel obliged to see something that's not on your personal A-list - no matter how famous.
If you do have a special need or interest, that's where this forum can be great. "Can anyone recommend a restaurant that serves gluten-free meals near the Louvre" or "where can I buy used CD's" are things that can be hard to get from a book.
