I highly recommend the Google Nexus tablets as they are very good entertainment devices at a very good price.
I own the first gen Nexus 7 (7")and and the Nexus 10 (10"). Video and sound is awsome on the Nexus 10, but it is a tad big to be carried around when you're mobile quite a bit.
The Nexus 7 has ok video quality but the audio kind of suffers due to no front face stereo speakers like the Nexus 10. This might be different with the new Nexus 7 (2013). It however can fit into my back packets on my pants so I can carry with me hands free so it's got more portability and feels good to be used with one or two hands. Just remember to take it out of your pocket before sitting down.
As for software, as the others have mention MX Player is a very good video player that's compatible with various video formats and it's free.
I recommend using the Utorrent app to download your anime first and then watch it on MX player. The low amount of ram and speed of ram on tablets can be poor compared to desktops so it makes watching streaming video unreliable.