I'm assuming you're gonna go for the $600 (the premium version if you will) one?
Will you be using it for games only, or will it become your main movie player (Blu-Ray movies?). If its the former, then you should actually be able to not even worry about DVI/HDMI, since as far as I know, the games are not encrypted with HDCP (since recording a game being played, at least so far isn't a big deal), and could make do with using the component inputs on a monitor, if it has them that is (also you can get component to VGA adapters). If you will want to watch Blu-Ray movies on it, then HDMI/DVI with HDCP compatibility is a must, in which case you'd probably be running your PC through VGA, and you'll want a monitor that doesn't look bad through that (some LCDs do, while others people can't even tell a difference between DVI and VGA).
I would not get any LCD TV under 27". The ones in the 15-26" size are typically very overpriced and most just aren't good monitors (some scrimp by using a panel with only 800x600 resolution, but cost more than what you can get a nice monitor of that size for).
How soon are you wanting to pick one up? Would you be able to wait until a lot closer to the PS3's launch? The reason I ask is that right now, there isn't a whole lot that would fit your needs, with the Dell 2007FWP being probably the prime one I can think of, and it seems to have some major issues with color banding right now. Most of the other 20" LCDs in that range are either not something I would recommend, or else aren't HDCP compliant. There is some good news though, and that is that prices in the 20" range have been falling, and probably will even further by that time. Not only that, but I would say its fairly likely that quite a bit of them will get updated with HCDP and/or new panels (or hopefully in the Dell case, major fixes to whatever is causing the problems). Also, the PS3 launch is close to Black Friday and just the holiday sales time, and you might be able to get a great deal on something around then, although it might be more hassle than its worth, and I wouldn't count on there being something worthwhile to get.
As for what you need to look for in a suitable monitors, I would say the primary thing is the reviews/general consensus of people who own or use that model. Specs can give you a reasonable idea of how good a monitor is, but they're often overblown if not downright wrong. I would definitely recommend picking up a monitor that is HDCP compliant. If at all possible, I would also recommend playing the waiting game for now, as there's bound to be something that fits your budget and needs better than whats out now.
A couple of other things to consider as well. How are you going to handle audio? Its quite possible that Sony might even release a DVI/VGA computer compatible cable, like Microsoft did with the 360. I would try to figure out what all I will need or want, figure out how much it would cost and then start saving like crazy for it.
I hope that was helpful for you.