Hi Arianna,
I just went through this same dilemma myself when I published my first book last month. Here's what I learned:
It's possible to publish directly to Kindle and Nook (Nook's version is called PubIt), which I recommend doing because you then have complete control over how the end product looks. You also have instant feedback on sales through their dashboards, which is very nice if you're impatient like I am.
I thought that I could publish to other formats on my own as well, but over time learned it wasn't as easy. You can only publish to iBooks if you have a Mac, otherwise you have to go through an aggregator like Smashwords. Kobo has a new service that supposedly allows authors to publish directly, but my experience was not good. They were slow to answer emails and they require an ISBN (which would cost $125 to buy yourself). And other readers, like Sony, don't allow authors to publish direct at all. I tried Google Books, since they sell ebooks, and that was a disaster that I don't care to repeat.
So in the end, I used Smashwords, and I'm pretty happy with it. Their meatgrinder wasn't as hard to get through as I had feared (formatting a Word doc takes a little time to get right, but it was worth the trouble). My ebook through them is less "pretty" (no images - it was too much hassle), but the words are all there, and that's what's most important. I'm still waiting for them to send the book to Sony and Kobo, but it went up on iBooks almost right away, and has been sent to Diesel and another one (I forget the name now).
As for ISBNs, that was an issue that had me confused at first. This is what I learned: you need one for sites like Kobo and iBooks, but not for Amazon or Nook. Those sites supply their own numbers (Amazon's is an ASIN and B&N's is called a BN ID). If you use Smashwords, they give you an ISBN for free. You can't use the Amazon ASIN or B&N"s ID on other sites, and can't use the SW ISBN outside of their service. However, if you do choose to buy an ISBN for your ebook, you would then be able to use it for all the different sites, since you would own it outright. But it costs $125 to buy one from Bowker.
I don't know as much about libraries, but I don't think every ebook on Kindle is available to libraries. The recent news about Kindle is that OverDrive (the major provider of library ebooks) now supports the Kindle device. But to get a book in OverDrive's catalog is probably a different matter entirely, and I don't know how friendly they are to self-pubs.
I hope that wasn't too confusing. I tend to get wordy when I try to explain things. I've been told I would be a terrible teacher.