The K400 is adequate for short text entry like when searching for shows. But the keyboard feel is rubbish compared to a desktop or even a laptop keyboard. Shouldn't be a problem unless you're planning to write an essay on it. Just be aware of what to expect. I dunno if the newer K400+ has improved on the K400, but its reviews seem to be slightly lower so probably not.
It uses a Logitech unifying receiver, so the price is almost worth it just for the receiver (receiver costs $8.50 on its own, keyboard is about $20-25, frequently goes on sale for $15-$20, was $10 this past Black Friday). I can confirm that the battery is phenomenal - mine went 3 years as well.
I suspect though that any wireless keyboard will work, as their USB interface seems to be universal (kinda has to be to be able to work in computer BIOSes without installing any drivers).