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I'd recommend the Nexus 7 (2nd gen, the 2013 version). It is very affordable ($225'ish), has over 300 dpi, pretty good battery life, and the 7" format makes it very portable (fits in the pockets of baggy jeans). Being a Google product, it always gets the latest Android versions, too. It's also powerful and can run non-simple games, too, and is beefy enough to serve as a competent chess partner.
It doesn't really have any competition at that price. I much prefer reading on my e-book devices, but the N7 is the only tablet that I felt somewhat comfortable reading books on due to the high resolution. I use mine for browsing and "light" work (such as answering mail when I'm on the couch), and I stream video wirelessly to it (from the laptop).
If you want something larger (and less portable), I'd wait for the Nexus 9. Long-term support is important to me, so for tablets I'd really only get a Nexus or an Apple product (but find them too expensive and too locked-in).
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