I bought one as soon as it became available in the UK. Was always interested in picking one up since launch but waited for it to be out here officially.
Essentially what it is, is a way to "smarten" your TV, I don't own any TV with dashboard stuff so that was my main reason. You need 1 HDMI port and a usb slot or a spare AC socket to use the usb AC adapter. Connect the dongle to the wireless network and access it via any smart device + PC/Laptop.
The chromecast app will list the majority of apps on the google play store that are updated to use chromcast and endorsed by google, anything there will pick up the chromecast on your network and allow you to stream anything on that app to the TV it's on.
The chromecast itself stream the data so it's not pulling anything from your phone. For example, if you want to watch a youtube video from your phone, go the the youtube app, tick the button to stream to TV and pick a video. The chromecast will stream the video itself so you can do other stuff on the phone and it will have the controls listed in the notifications bar. I use it a lot to stream youtube and BBC iplayer mainly.
The video quality is automatically changed by how much bandwidth it can use. I've noticed on the crunchyroll app though that it will use a static video quality that I don't have the speed to handle and you can't change it manually yet. So it comes down to how good the app is.
The best feature in my opinion is being able to stream any webpage from google chrome. It should automatically find the cast and allow you to stream any page. If you're watching a twitch stream for example, full screen the stream and it will do the same on your TV. It's really nice. I've also used the browser to stream mp4 and other poop for anime but you'll need something like
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for MKV.
As long as you have a good quality router and enough bandwidth, you shouldn't notice much compression. I don't have a good internet connection so I can't really confirm that though.