Hi!
There seems to have many options, but I bought a kindle and I absolutely love it! I search and buy the books from Amazon (thats where you get the kindle books) , it downloads automatically to my kindle, and I can sync it with both our iPhones and iPad, and I can also read it on my laptop. It's a delight.
I do have other readers, but I don't even use it (like the iBook that comes with the iPad). With Amazon-kindle I have always found every book I wanted... And if I want to "carry" any personal documents around, I save them as a PDF and send it to my kindle as well (I use different PDF creators, but anyone will do I think). I found a book available only online, but I saved the page as PDF and voilá, it's in my kindle as well.
And by the way, despite the dozen options we have for book readers, I prefer the simple, basic, black and white only, kindle. If I want colors, I read on the iPad. Reading on a kindle is SO different, so much easier on your eyes, and it really looks like an ordinary book page. I'm sold.