It’d be interesting to see how you get on with this. I love Apple’s stuff, but if you don’t use it “their way” it can be a pig. A quick Google suggests that even Apple’s own Apple TV can’t – or at least isn’t designed to – connect to media backed up using Time Machine or on a Time Capsule.
I’m assuming you are already in the Apple eco-system. If so, I can recommend using iTunes Home Sharing in combination with Apple TV. It will mean converting your media to an Apple-recognised format which may put you off, but I love it. I can access all my media on any (Apple) device on my home network including my TV.
[EDIT – I did try the DLNA route using my BD Player and Twonky Media Server, but found it was a poor experience]