I have the Dell 2405fpw 24" monitor you speak of. The monitor can handle any resolution under 1920x1200. 1920x1080 will only fill most of the screen. However, this monitor has a cool feature, like most big screens, that allows you to stretch the image to fill the screen. In the image properties, you can choose 1:1 ratio, aspect ratio, or "fill".
1:1 will display only the exact size of the original resolution; this includes games. I can play an older game that displays at 648x480 and it'll only show on part of the screen.
Aspect ratio will stretch the image, no matter the size, to maintain either an 16:9 ratio or 4:3 ratio. If you're watching television over the component input, for example, and you set the output of the cable box to 1080i then the monitor will keep the aspect ratio of the output. 1080i is defined as 16:9 ratio (1920x1080). 1080p simply means that the image is progressive and all pixels are processed at the same time instead of every other line (odd then even or vice versa). A game or regular television broadcast that uses 4:3 ratio will only show in the middle of the screen, but will go to the top. 4 is the width and 3 is the height.
When using "fill", you're essentially stretching any image to fit the monitor's ratio of 16:10. 16 is the width and 10 is the height. 16:9 ratio would then be stretched taller to fit the screen. 4:3 would then be stretched much wider and everyone looks really chubby. =)
16:9 only looks funny on a 16:10 monitor if the film isn't true 16:9 but instead filmed on a much wider film. I'm sure you've seen them. They're the ones that have much thicker black bars on the top and bottom than other films. 16:9 is simply an average of all the ratio types, not the rule. Of course, there are many that are and so it's no problem.
Also, games that aren't natively widescreen will look really wide if you using "fill" instead of "aspect". However, there are many games that are and so you don't have to worry.
As for HDCP, that's where this monitor lacks. It has no HDCP processing. The 2407 introduced that much needed feature. I bought this monitor before HDCP was in wide use. I knew I need it eventually, but instead of spending twice as much (at the time) for an HDCP capable monitor, I decided to spend less and then sell this monitor or use it on a computer exclusively and buy another one that has it.
In other words, any source that requires HDCP to view the image, then you're out of luck. HDDVD and Bluray both require HDCP, no matter how you view them (computer or component box). On the other hand, you can bypass HDCP on both methods, however, you'll supposedly lose quality. On computer, you can use a VGA cable instead of DVI and you'll be able to view most titles this way. However, in some cases you won't. Instead, it's better to just purchase a copy of AnyDVD HD. It detects any disc with HDCP encryption and removes it while you view it. Not everyone has an HDCP capable monitor and so this is the workaround for computer. Of course, only use real movies on the original discs or you'll run into trouble, both with the law and with future software.
As for component boxes, you can watch the movies over component cables (RGB) but the signal isn't the same quality as it is over HDMI or DVI. First of all, digital vs analog quality is obvious, however, as part of the standard and security measures, HD movies with HDCP require that the resolution of the signal over an analog connection be lowered to discourage piracy. Sure, you can view the movie but it won't be true 1080p. Of course, I'm sure there are models that allow for viewing over a VGA cable or something but I haven't done any research on that yet. I'm sure there are people on here that have.
My advice? I would stick to watching them on the PC and then just output the sound over a 7.1 channel HQ sound card to your receiver. AnyDVD HD works flawlessly. All you need past that is to purchase a Bluray/HDDVD software player. I assume you already have a drive. If not, there are combo read only drives for around $230. I know you can get a bluray/dvd burner for $150. I'd get the $230 drive because it's going to be awhile before they can remake all the HDDVDs into Blurays and I'm sure there will still be HDDVDs for quite some time. I'm certain HDDVDs will be cheaper than Blurays, of course they always have been from the start. Keep in mind that Bluray has pretty much conquered HDDVD. Toshiba bowed out (co-founder of HDDVD).
Anyhoo, thanks for reading and good luck.