I run Aldiko on my tablet. Works pretty good. Another option is the Overdrive client if your local library supports it. I have checked out many a book and read it in the app without any issues.
As for what to read…that depends on your tastes. I know that Aldiko has the Feedbooks option you can check out. Doing a search on the Net can probably find you all sorts of creative commons things.
I follow this site which lists free commercial ebooks for the Kindle. Since I don’t actually own a Kindle, I use the free Amazon Kindle PC app to download them and then convert them to DRM-free epubs. (Note that this may be illegal in some places.)
You probably know about it, but all of Cory’s books are here:
Project Gutenberg has all kinds of great material. O. Henry’s forever worth a read, and there’s some Wodehouse novels which are pretty much the best things ever (and he’s one of Douglas Adams’ inspirations).
There’s a version of Hedgehog Art Through the Ages here (though on pdf) that is both educational and fascinating. Critics are calling it the best hedgehog art history book of 2016.
(it might inspire you to one day pick up a paper copy which is even more delightful to peruse)
#bookz on IRC. I used this once having never used an IRC client before and my book popped right up. this is massive libraries of things you would otherwise have to pay for, if you catch my drift. Here is a guide that explains it. http://www.geocities.ws/prissy_90/Media/Texts/BookzHelp19kb.htm
I know of an even more “for dummies” version if you need it.
I don’t actually read a lot of ebooks, I just had to find all this stuff once for something special. So, I used Calibre to read it. No idea about MR or the other, sorry.
I have a knack for “finding” non-free epubs, so sometimes I read those.
But for CC stuff, what I often do is find interesting documents from Media Archive. One problem with this is that a lot of books - or, at least the ones I happen to be looking for - are often badly OCR’d from scanned paper, automatically generated with no corrections applied. So every so often what I do is patiently OCR the PDF version and correct everything in LibreOffice Writer. So I am basically transcribing the book as I read it. Then I use a plugin called eLAIX to export the Writer document to an epub file I can load onto my reader for next time. And/or release on the interwebs for others who want a decent copy which is actually readable.
It’s a bit of bother, but I often think worth doing.
Just putting this here in case anyone else is like me, in NY State. If you are a citizen of NY you can get a card for the NYC public library system. Just go on their website to sign up. I think maybe there is a small fee? Anyway, you can use Overdrive and have access to their whole lending library on your e-reader.