1080p still requires fairly beefy or optimized equipment. I don't know all the technical details, but I have played around with different devices and experimented with different kinds of 1080p formats, and many of the devices that claim to do it have issues. Sometimes it is stuttering, sometimes it is weird slow-motion effects, some have issues seeking. Most full size pc graphics cards don't have an issue with it. raspberry pi i'm pretty sure won't be able to play many of the files I'm talking about. I bought a little android htpc stick (see the gadget thread) which claimed to be able to do it, but it couldn't (stuttered a lot).
I will give a huge

to this little chinese device that seems to have no problem playing back 1080p. All you need is to attach a usb drive to it and it will do the rest. It's only $60 and I take it with me everywhere. It's from a company called Diyomate.

Now, your tv probably has multiple inputs. Put the diyomate on one input, this will be where you watch all your movies. For your internet requirement, get the android stick i was talking about, called the mk808b:

Now, to control the internet from that android interface, you need some kind of airmouse. I've heard the gyration and mx air will work with it, but I haven't confirmed it. But sticking to this chinese theme, you can buy a cheap airmouse that does work well, called the rc11:

The remote has a keyboard on it to boot. The more expensive and better quality option is the gyration mouse/keyboard combo.
But using this route, you get everything you want, and it costs total under $200.