Connecting Macbook Air 2011 to HP LP2475w monitor.. use DVI, HDMI or Display Port?
I have this monitor since 2008. My experience with a MacBook Pro 13" (early 2011) is:

HDMI

Any cable will do it, but you'll have to override the Mac OS X settings to force RGB mode. To do that follow the instructions in

http://ireckon.net/2013/03/force-rgb-mode-in-mac-os-x-to-fix-the-picture-quality-of-an-external-monitor

DVI

No problem, but only with Apple's official adaptor + DVI to DVI cable. In this case, image quality is perfect and I haven't got issues waking from sleep. I also tried with a 43€ mini DisplayPort to DVI 1m cable from Clicktronic and I saw random red and green pixels on dark areas of the screen. I also observed this issue with another mini DisplayPort to DVI cable from a different (cheaper) manufacturer.

DisplayPort

Using CA's mini DisplayPort to DisplayPort cable I have extremely annoying jitters and shakes on the screen. In between those, the image quality is perfect but overall renders the usage annoying. It looks like it gets better as the monitor stays turned on for some time (about an hour). I've also observed issues when waking from sleep. Apparently the problem is not the cable, and reports of good compatibility do exist.

http://estore.circuitassembly.com/products/mini-displayport-to-displayport-adapter-cable-1m.html