I have an ipad and a kindle.
I like the ipad for reading because it has the back light, so you can read in bed. Yes, you can get a nook/kindle with a back light now and I would highly recommend that you do.
I also have a kindle that my mom gave me when she upgraded to the kindle fire. I love my kindle because it is so small and it is easy to carry everywhere with me, the only downside is that (like someone else said) to go back a few pages is harder to do then a device that you can use your finger (ipad, kindle fire etc). The regular kindle has buttons on the side that you use to change the page. After using an ipad for so long and then using a kindle it took me a little bit to get used to the fact that I can't touch the screen although I still find myself touching the screen to change the page.
You will need some internet access for the kindle to download books or to search books etc.
I love the kindle because I can get on amazon and look up books and download it onto my kindle from there. So some days I will download 5+ books. Also if you have amazon prime you can borrow one book every month from the amazon library for free and that is nice.
My mom had both a nook and a kindle and she preferred the kindle but I'm not sure why. I would try and find someone who has one of each and play around with it and see which you like more.
I would like a kindle fire-mainly for the fact that it's like a tablet and my husband doesn't like to share the ipad. But if you want something strictly for reading then the kindle and nook is the way to go.
If you are looking for free or discount books sign up for http://www.bookbub.com/ebook-deals
I LOVE THIS SITE. You can pick the genres that you like and just about every day it will send you a list of what books are free of extremely cheap that you can buy and you can have it sent directly to your device. I know you can do this for the nook but most of the stuff that I have seen is for the ipad or the kindle.
As for your eyes hurting when reading from a computer screen, I get that but with the kindle I don't have that problem. Also with the kindle and a tablet you can change the font size and make it bigger if you need to.
Hope this helps.