What's your recommendation for a good media-playing device?

I swore I would never do this, but I find myself looking for a device on which to play .avi and other video files, and which would also be good for internet radio and to play DVDs. I don’t need it to surf or check mail, or to do anything that necessitates a physical keyboard. I’d like it to have a large screen, but also not break the bank (which I realize might mean shopping for a used one – that would be fine). I have external speakers, so the sound system is not critical.

Additionally, are there any pitfalls that await me? Anything you would do differently from your first purchase?

Do these things tend to come with built in or external stands, or is that something that would have to be purchased separately?

I’ve never owned a tablet/iPad, so I’m not quite sure how to shop for this and am open to any suggestions. Thoughts?