Yeah, Apple TV is great. Really great. But beyond that, the best all-around streaming video box for most people absolutely is the Roku.
So you're cutting the cable TV cord. Good for you. And while we love Apple TV — those screen savers and easy AirPlay!!! — you can't help that it's missing services like Amazon video, and Google content, if someone in your house swings that way. Which streaming box is the best for more people? Easy answer. For most folks, Roku is going to be the best bang for your buck.
First: Why a Roku? It pretty much has every streaming service available. (Everything except Apple content because Apple is why we can't have nice things.) It's got PlayStation Vue. Sling. Amazon. Google. Netflix. Chromecast. YouTube. So many different "channels" that for as long as I've had a Roku I feel like I've barely scratched the surface. (DirecTV Now is listed as coming eventually.)
Why a Roku Ultra, though, when there are sticks for a third of the cost? You get what you pay for. Yeah, the stick is cheap and can do a decent job, but if you want 4K resolution and HDR and USB media and a better remote and private listening and ... Basically it's way more future proof, and tended to handle the streams for me better. If you just want a test of how all this works, fine. A stick will do. But if you're serious about it, it's worth spending the extra money.