I'm not sure you know why video editors need two monitors. Now there is an issue with the landscape. NLE's pack a lot of separate modules for all the assorted editing tasks onto the computer screen. There's the timeline, media bins, trimming tools, color corrections, preview window; the list goes on & on. So it is nice to have two monitors on your computer so you can spread things out instead of stacking them. So I'd say that getting the two 19" monitors would make it easier to keep track of everything. But computer monitors can't do the one task an editor needs the most.
Video editors need to view their programs on a video monitor. SD or HD televisions are the target screens for the majority of videos. And they operate differently than computer monitors. So you can't accurately judge color or sharpness (and bleeding) from a computer monitor. You need to be viewing the video "program out" signal using something designed for that signal. But first you have to investigate how your NLE generates your "program out" video signal.
It seems the majority of NLE's with a "program out" use the Firewire (or IEEE1394) port to send that "program out" to a video monitor.  I found that to purchase a video monitor with a Firewire in connection was prohibitively expensive. So I run the IEEE 1394 cable to my camcorder, then I can connect the camcorder's video outputs to an NTSC video monitor. Now I can tell when my text is too small or the text color & outline colors clash (or blend into soft edges.) I can make color corrections to improve the look or to match color shifts between scenes (and especially between shots.)
Now you have an extra factor to consider in selecting your program monitor. You are planning on editing HD video. First, let's clear up a bit of confusion around HD monitors and widescreen computer monitors. They are two different things. What makes them different is what kind of signal they expect (and can actually take.) To the computer, 4:3 and 16:9 aspect ratios are the only difference between SD and HD video. Widescreen computer monitors are ordinary monitors but with the wider aspect ratio of HD video. However with video monitors, there are worlds of difference between SD and HD televisions. In the modern lingo, an SD video signal would be called 720x480 30i. While the digital broadcast HD signal is 1080x720 30i. They are so different, you can't even use the SD video cable to send the HD signal to a TV. But my Digital TV tuner can convert the digital HD signal into something my analogue TV can accept. So while I have an analogue TV set, I've been watching the Olympics in HD, sorta. I get a letterboxed, 16:9 image on my 4:3 television (plus really great surround sound.) It is just like when I watch 16:9 SD video (like from a DVD.)
So let's take a moment & review. We can watch widescreen (or 16:9) or normal (4:3) video on any monitor. This includes computer monitors as well as TV sets. But to see an HD video, we have to have an HD monitor. And feed it an HD signal. So without a BlueRay DVD player, we can have an HD TV but we'll see only SD signals from the DVD player. Although on the HD set we can see the whole image without letterboxing. But there are upconvert DVD players that add a bit so the SD video looks more like HD video. So we can summarize the functional difference between SD & HD by the connection each requires. SD video can travel through a simple two strand (signal & ground) wire into an RCA connector. But the HD signal requires a multi-strand wire & multi-pin connectors.
And finally, I can respond to your question about monitors. If you intend to produce videos for anything other than the web, two monitors are required (for professional results.)  Of course, one monitor has to be a computer monitor. The other monitor needs to have inputs for the kind of video you expect to be making. If you're making HD video for BlueRay DVD's or to watch from an HD device, typically your camcorder, you'll want the second monitor to accept the HD signal. Now if you are making videos you'll watch from a standard DVD, you'll really want to have your monitor set for SD viewing, even though the 16:9 signal will be letterboxed on that monitor.  Now I know some widescreen monitors can take a variety of input signals. So if your computer monitors have inputs your camcorder can use, then you can dedicate one of them to be your program out monitor from the NLE and the second monitor will be for the computer. But don't be fooled by any extra connections from your computer. (I have both an S-video & monitor out on my laptop, but both displays are actually part of my computer desktop.) The program out signal is generated by the NLE (not by the computer OS) and needs to be connected to a display that takes some sort of NTSC signal.
So now, if you're confused about the issue, ask me about it again. I'm not sure my posting is entirely logical. The facts are accurate but their organization isn't so great. Hope it helps. And good luck with your new edit suite.