This is, unfortunately, a sort of biased answer but with good reason! I back my answers with the sources given to you.
The reason I say my answer is biased is because I'm a big Canon fan. Their DSLR's are fantastic for recording video, believe it or not. If my sources are correct, I think an entire season of House was filmed using a Canon 7D, a $1,700 camera. However, that's way above our price range.
What you want is something along the lines of the t2i, t3i, or the 60D. Between the t2i and the t3i, you have a price difference of about $150. Now, the only actual difference between the two is the maneuverable screen that flips out. This handles great for video. However, whether it's really worth that extra $150 is up to you. These shoot great videos in 1080p resolution and they're a lot cheaper than what you're looking for!
But if you want to push that limit up to $1000, the 60D is the way to go. The 60D is essentially a tier up from the Rebel T series. Thus, you're going to see the flip-out screen, a larger viewfinder, faster shutter speeds, more color depth, and better battery life. It's definitely the camera to wield with the proper usage. I don't really recommend it for use as a starting camera but it will fit your purposes perfectly.
If you want samples of videos, I suggest looking at Youtube videos filmed with these cameras and see for yourself. Sorry I can't give you much on Nikon's, the other major DSLR brand, but I hope this knowledge helps!
We are happy to present the famous Nikon D90 DX 12.3MP Digital SLR Camera with 18-55mm f/3.5-5.6G AF-S DX VR Nikkor Zoom Lens + 8GB Deluxe Accessory Kit.With so many on offer these days it is great to have a brand you can recognise. The Nikon D90 ...
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With this one they boast the "Worlds1st consumer HD video camera w/ continuous Phase Detect AF" which is going to be a really nice feature for you (continuous auto focus). It can also do continuous 10 fps shooting. It shoots full HD video.
They have employed a relatively new technology on this model which is pretty cool.... a Translucent Mirror. So the a55V can feed both the image sensor and the Phase Detection at the same time, resulting in fantastic pictures and video.
Apparently gets really nice pictures... you should look at the link.
Capture your perfect moments with the world’s first Translucent Mirror Technology DSLR enabling simultaneous focusing and capture. Continuous shooting is 7 frames per second, complete with continuous auto focus. Auto focus is also visibly faster...
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Amazing auto focus capabilities. Nice small size if you travel a lot/ shoot on the go. Can also auto focus while shooting video, which is a major plus. Compatible with Sony's a lenses, Minolta lenses, and Konica Minolta AF lenses which gives you some options. Also, a nice price if you're just starting out.
Kit includes:♦ 1) Canon EOS Rebel T3i Digital SLR Camera Body & EF-S 18-55mm IS II Lens♦ 2) Canon EF 75-300mm f/4-5.6 III Zoom LensThe Canon EOS Rebel T3i features Canon's DIGIC 4 Image Processor and an 18.0 Megapixel CMOS Image Sensor. Other cutt...
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Like Joshua said the biggest difference between the t3i and t2i is the articulating LCD screen on the t3. Other than that you get the same image processor, although this little package does have a nice telephoto lens while still keeping it under priced.
Not only is this camera great for stills and video but it is also excellent overall. This camera is well made and has great HD video features including manual exposure control. It will also treat you well in both light or dim environments offering an expandable ISO range of up to 12,800. You're getting 18 MP with a speedy processor and 3.7 fps continuous shooting. It's a great camera for your price range.