The Hanns is the cheapest, however, it does not have DVI, and the PS3 would be using the HDMI. So I would be missing out on quality for my computer?
The BenQ has DVI, is more expensive, but is 700:1 instead of 1000:1, so the quality isn't as good as the BenQ?
The Sceptre has both DVI and is 1200:1. However, I've heard many horror stories about their monitors.
What is my best bet in this situation?
Also, what about using a different connection like DVI with hdcp for my ps3? Would I be losing quality on my ps3?
If I do decide to go forward with this setup, what kind of cords do I need for the best quality?
Among the top 3 monitors, although they do produce good quality you wouldn't be able to "harness the full potential of a PS3". Their maximum resolutions are 1600x1050, while the output the ps3 produces is 1900x1080. To get this resolution you would need to sped a bit more for a 24" monitor, as that is the smallest size that supports the resolution for 1080p.
Right now, the PS3 only has games that output 720p, but as time goes on, it will have many that output 1080p. So, you wouldn't recognize the loss of quality until later.
On a side note; I'm sure you could get HDMI to DVI cables or DVI to HDMI cables, whichever you need. However, I don't think 1080p is supported with DVI cables, so you will most likely experience a signal quality loss when going from HDMI to DVI.