No, it's not going to be in the kit. You'll have to furnish that yourself.
Also, no, you won't be as happy with the $300 headset as you would be with a more expensive one. However, people's heads vary and you might prefer one model over another, so I'd suggest trying several different kinds before committing.
That said, I really like my Lightspeed Zulu. And a friend liked it enough to buy one of her own just after getting her private pilot's license. We both thought they were worth the money. I have a last-generation Pilot ANR for my other front-seat headset and I can definitely tell the difference.
All in all, I'd recommend waiting until you're getting close to flying before buying one, just to pick up any technology improvements that might come out. And at that time, when you're getting current again, try different types before buying.
Dave