OK I can help with this, I have a PS3 and I have it hooked up to my 22" Samsung 225BW, The same screen that my docked laptop and desktop connect to (albeit those do through VGA KVM). The video connection is made through an
HDMI to DVI gold plated cable I got a short one for something like $5 shipped and It works great and here is why:
The Samsung 225BW supports HDCP This is VERY IMPORTANT, any monitor that is capable of receiving signal over HDMI / HDMi-DVI is HDCP capable. Lucky for you the HP monitor you are picking does support HDCP however one thing to keep in mind.
However I can't garuantee that your monitor would be able to handle 1080p resolution you might have to go down to 720p which is not good if you can do something about it, in my case all my games except for UTIII are 1080p, so it matters for me.
It's true that my monitor's max resolution is 1680x1050, however I can set my PS3 to 1080p (1920x1080) and the monitor auto scales the video input and it outputs a nice sharp picture as if the monitor natively supports 1920x1080, actually on the screen's menu if you look it says it's a 1920x1080 signal
One issue you will run into is that the audio output must be rerouted in the system config from HDMI (since most monitors don't support AUDIO through DVI-D) to optical out to optical in or line out into line in. I have a creative sound card connected to my small IBM desktop, so I just set the audio output to optical on the PS3 and run a short optical cable to the sound card's optical in and through that to my Desktop Speakers / Headphones, that small desktop is running 24/7 so I don't have to worry about turning it on everytime I need to frag some suckas on COD
The only issue that I ever ran into is that since 1920x1080/1080p is not a native resolution, every time the game or the PS3 enters 1920x1080 / 1080p mode a little error message pops on the screen telling me that the res is not optimal....that goes away with single press of a monitor button it's not that annoying but I can deal with that popping once every hour or two whenever I am switching between games.
I keep hearing that there is a way to disable this little annoyance but I didn't figure out how yet....I'll keep looking I guess.