I have the newer Dell 24" (2407WFP). I just hook in the VGA cable, and run an optical cable from the VGA cable out to my Logitech decoder. If you have to buy an optical cable - your only option for VGA - check monoprice.com (very inexpensive, the site most people use) or bluejeanscable.com ("Monster" quality at a fraction of the price, the fastest shipping I've experiened from an online retailer).
If you want to use component cables, that's fine too, and you won't need to buy seperate audio cables...unless you need an extension so they reach your sound system, which is actually quite likely unless your sound setup is within inches.
Only thing to keep in mind here is that you should try to get a monitor that matches one of the 360's native resolutions. MS has updated the 360 to support more resolutions in the past, and I hope they continue to do so because mine is not supported, and I'm not alone. SEVERAL of the native resolutions most common in widescreen monitors, including 1440x900, 1680x1050, and 1920x1200. It'll still look great (experiment with resolutions closest to your own if you don't have your native resolution supported), but it won't be "pixel perfect" and you will notice a very small amount of stretching/blurring if you're looking for it. Here are the supported native resolutions (widescreen and standard):
640×480
848×480
1024×768
1280×720
1280×768
1280×1024
1360×768
1920×1080
Don't let that deter you though, it's not that big a deal for most people and the majority of people won't notice it. I'm pretty picky about stuff like that and it doesn't even bother me unless I'm in a shitty mood.