Mac Mini is a great (but expensive) solution if you want to use your TV as a computer monitor basically. Looks smart, very small, very low power consumption.
There is an app called Plex (also available for PC/linux I think, I just prefer Macs) that will turn it into a media server. One of the best things about this is it can serve up films/tv shows/music to all your other devices e.g. phone, tablet, other computers, even Raspberry Pi (which makes an awesome low cost media player).
Is TV the best idea for browsing, email, etc. though, seeing as you’d need a mouse/keyboard etc. Would a tablet not be a better idea? You have portability, touch screen input, plus not tying up the TV for other family members.