I have a Kindle.
That is the physical item on which one reads the mobi file type.
I also have the Kindle software on my computer and smart phone too.
On Wikipedia you will find a list of e-reader types, the software and the files they will run. There is a programme called Calliber which will convert one file type to another.
My smart phone came with Kobo e-reader software already loaded. You can read e-pub files on it. I like having the odd book on my phone for short train journeys.
Many of the sites with free (out of copyright) books now offer you a choice of file type. You choose which to download.
However, outside the USA the Kindle and Mobi files are not as universal. It is easier for instance to find Russian language books in e-pub. But that is no worry as you can convert them if you want to read them on a Kindle.
OH and I bought Kindles because the i pad is not good for reading out of doors in bright sunshine, and because the Kindle is cheaper so we can have one each. But you dont get colour on a Kindle, it is designed for text, so think about what sort of books you want to read. But it is an absolute blessing to be able to go on holiday as we just did without having to pack any books. And it is brilliant being able to buy books over wi-fi while travelling. You dont run out of things to read.
Looking for free books and observing copyright is a bit of an art. For many English language classics, Project Guttenberg is a good starting point. I know a site for Russian books. I guess you just need to Google and experiment?
I bought a Kindle for my grand daughter and got hold of all the classics I wanted for her. If you want something specialist like classic books on horsemanship, or exploration, it is harder, but there are some good things out there.
