Apple TV question

Netflix is a subscription based service, that right now gives you the most bang for your money. For a few bucks per month, you have loads and loads of TV series, and movies. In some cases, you have to keep track of which movies you want to watch, as a great deal has been licensed for only an x amount of time. Also older movies and TV shows come and go (again depending on licensing deals struck with studios).
Self-produced shows though, are there to stay forever (Stranger Things, Orange is the New Black, etc etc).
Please carefully take note of the differences and choose accordingly:
https://www.netflix.com/signup/planform

After that, go into the Apple TV, and download the Netflix app. All you need now, is to input your Netflix username and password, and you're good to go.

Besides buying stuff on iTunes?
Depending on your location, more similar streaming services (CBS All Access, Hulu and what not). All monthly subscriptions, slightly less bang for your money as Netflix.
Maybe one or two are truly free, if for instance you're in the States, the CW app might be totally free. Others like NBC, CBS, have some restrictions, but still a lot is free (usually the episode that aired the day before).

Roku and Chromecast are much cheaper.

Roku allows other services that are "free" as well as paid services.  Roku is basically a linux media player box.  If you created your own linux box, you could have it set up with similar features as a Roku.  In fact you'd have more, since you'd have a full blow linux OS desktop.  You can install hardware to work with a remote control too.

Chromecast relies on any computer running chrome to send a video to it.  It works great with Youtube videos as well as any streaming web site, but it's not a stand-alone device.  You must use a computer with Chrome to cast your browser tab or desktop.  Browser tab will actually play quite well, since Chromecast uses the desktop browser as a controller, not an actual cast with streams from the desktop.  Unfortunately, when you cast the full desktop to a Chromecast to play videos on VLC, it will lag a little compared to the desktop.  The stream will play smoothly, but there is a noticeable lag if you're doing something interactive.

Apple TV is proprietary to Apple and cost the most for similar features.  You can use the services directly on the Apple TV, but you'll have to pay extra for the services.  If you're in Europe, you can go visit download and streaming sites on your apple computer,  then you can use Airplay to send them to the Apple TV.  You could do it in the USA, but many of those are technically not legal for Americans to use.  Airplay is the only way to really get "free" videos to your Apple TV, but you'll need a Mac.  Airplay is much smoother than Chromecast when you cast the entire desktop.

I see no real advantage to the Apple TV, if you already have a smart TV with most of those built in services already.  I'd only use it for Airplay, but Chromecast is much cheaper and works with any computer that runs Chrome browser (e.g. Windows & Linux).  Since it was a gift, you didn't pay that premium, but your gift giver did.

If you have a "dumb" TV, then it makes sense to get one of these, but Apple TV really only makes sense if you have Macs in your environment already.

You can use your iPhone to do Airplay to the Apple TV.  That's basically it, unless you want to subscribe to additional features. The Apple remote and interface are definitely smoother and better than the others, but you do pay a premium for high margin Apple devices.  If you install chrome on your iphone, you could Chromecast too, that's why I would get a Chromecast in a mixed environment, if a choice were available.