If you're going with uncompressed or lossless compressed video, then write speed and capacity is important to consider. If you're planning on real time recording with high quality lossy H.264, then write speed or capacity doesn't matter much, the CPU does.
SATA III is compatible with SATA II and SATA I, if I recall. If you don't have a SATA III-compatible motherboard, you just won't be able to take advantage of SATA III's features.
The first hard drive you have listed is the exact one I have dedicated for videos and so far, I haven't had any problems with it. It reads and writes at about 130 MB per second through tests I've done at the beginning of this hard drive (it'll get slower as the drive gets more and more filled). This was done in the form of memory dumps which is pretty close to what uncompressed video recording is. A memory dump is basically loading a large amount of data (several dozen MB to a few hundred MB) into RAM then writing this all to the hard drive several times, noting how long it takes to save. This is without a RAID setup. If you get 2 of these and set them up for RAID 0, you could practically double the already high write speed. I've never used RAID in any form so I can't really answer much on that front.
To determine the speed you'll need, it's only a matter of knowing what video size and frame rate you'll be recording at - it's just multiplying... large numbers. The formula is quite easy: "VideoWidth*VideoHeight*FrameRate*3". For 1920x1080 video at 29.97 fps, you'll need a sustained data rate of 186,437,376 bytes per second. If the hard drive can't keep up, null frames are inserted which may cause slightly jerky video. This is where lossless video compression comes in which typically halves that, but that comes at a cost as it increases the workload on the CPU.
The others I don't have experience with. Given the reviews, I would stay away from that third one. The second one doesn't look too bad. The first one (the one I have), is only SATA II. The second is SATA III. So basically, it's a toss up between the first 2.