Optimal internet connection speed for Apple TV?

I've been thinking about an Apple TV for a media centre as a cheaper option than a Mac mini - currently we use a PS3, but I'd like to rent and buy stuff from iTunes.

However, we live out in the country, and our home broadband is only 4Mb. As the Apple TV uses iCloud for everything and has no internal storage, is this internet connection fast enough to stream HD content from iTunes?

 

Thanks for those specs.

Yeah, HD streaming via YouTube seems fine, but I can't really stream HD trailers from Apple.

So my question is: assuming all my devices are using the same iTunes account, if I access the iTunes store via the Apple TV and make some rentals and purchases, aren't the files downloaded to my main computer anyway?

So even though I can't stream HD over the net, I can just wait until the downloads are finished in iTunes on my Macbook Air, and then stream to the Apple TV from that over my home wireless network (with Home Sharing turned on in iTunes).

Is that correct?

I have a whole lot of HD .mp4 videos in iTunes at the moment anyway, which I am assuming can be accessed over my home wifi with the Apple TV anyway.

Instead of being "instant-on-demand" with the Apple TV, over our slow internet connection it would be more like rent/buy, then wait until everything has downloaded.