In regards to the tablet, I’m thinking about buying an Amazon Fire HD 8 though I’m open to any and all recommendations.
As for the distro, I’m fine with Ubuntu or Linux Mint (or for that matter anything that you may recommend).
For the ebook reading software, I’m leaning towards using Foliate since it supports kindle, epub, and pdf formats, not to mention that the UI is great and intuitive.
I know this isn’t the type of answer that you want to hear, but I really love my kindle. It may not be open-source but it works and I can upload books to it from my personal collection. And the battery life is much longer than an ordinary tablet.
If you want to have something to tinker with then I have heard that the open book project is a pretty good build it yourself alternative.