Short answer, you can't.
Barely anything whatsoever (Other than $10,000+ professional equipment) at the moment can record in higher than 1080p video - well, I have seen a few consumer products that "can" record at higher resolutions, but it is just digital magnification / the actual quality is beyond poor.
As for streaming, I can't even imagine what the required bandwidth would be. (but I guess it is usable - just wouldn't expect many sites to offer it for free).
Anything that can record natively at above 1080p is just far to expensive at the moment... And you will need the graphics horsepower to be able to play it back - there are no consumer players out there able to view it (computers are usually just an after thought) so without the entire eco-system, it just won't be popular for some time.
What I would recommend you do is get a good player that supports multi screens and upscale the content to play across all of them.
I know it isn't really what you want to hear, but I think until Quad HD becomes mainstream, it is going to be pretty much the best you can do.