the time capsule is just a file server (not media), so it's only going to send files to a computer.
Where did you get your files, really only 2 answers that matter... iTunes or other
if it's
iTunes, you need an apple TV or other apple device to play them back.
Your Mac will need to be on and running iTunes to stream the media, or most things you can stream directly from apple.
if it's
other, you have more options.
I recommend
Plex
It's a media server that will run on your mac. It will grab the files off your time capsule and send it off to the different clients.
if the file is not compatible with the player, the server will convert and stream as you watch it.
there are a ton of clients... mac, windows, linux, roku, chromecast, iOS and android as well as some smart TVs
This is a pretty easy workaround to get this running on the aTV, you can re-direct the trailers app to Plex instead. (check out PlexConnect) It's pretty nice, i use it on one of my TVs
you can also run the client on your mac, and get a nice interface that you can use from the couch
any of the media boxes (aTV, roku, chromecast) will also give you netflix, hulu, HBOgo, and lots of other channels (they vary by device, so check them out and see if the offerings on one stand out to you)
or you could just go with a smartTV. Plex supports
DLNA which is on most smartTVs even if they don't have a plex client, Most of them will also have netflix if not more options.
The DLNA interface is not as nice as a native plex client though, and might be missing some features, like remembering where you stopped watching something when you come back to it.
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i would buy 2 devices one for living and one for basement, they are all $99 or less. you're still way less than a mini.
all of them have a "10 foot interface" meaning they're designed to be run from the couch using a basic remote. and tend to be easier for the non-tech minded people in our lives to figure out.