There are obvious cases where old hardware is not capable of doing something that you want. But that isn't the case here. The OP wrote:
"So I wanted to give Apple's new series a try and I couldn't find any menu on my Apple TV (3rd gen)"
The fact is, Planet of the Apps is available on the Apple TV3, he just couldn't find it. The solution does not require a hardware upgrade.
Can anyone let me know where? I have a ATV3, and I could watch the first episode, but don't know how to watch subsequent episodes on the ATV. You cant airplay them, and they don't appear in TV Shows or movies.