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.
Get some older tablet with a relatively open Android build on it like 4.4.x and put on FB Reader. I see Moon Reader touted a lot, FB Reader is at least as good and isn’t full of advertising and nag popups like Moon Reader. And you can link it to your Calibre library via OPDS.