My personal opinion is to start with the best CPU chip I can afford.
Then, I'd mate it to a motherboard that both satisfies: whether it will make good use of such a chip and if I can afford the board.
I would then get decent RAM, but I'd settle for no less than 1 Gb, as most often, lack of RAM is a speed bottleneck.
Next comes the video card. I'd recommend not to scrimp here, as this handles your pictures and you want that not to lag. I'm not a serious gamer, so I'd settle for the next best thing to the hottest one around, or even half to one level below next best.
I would also get all the HD I can afford, as most people run out of room much faster than they realize. Many years ago, I thought my 15 Gb IDE HD was the cat's meow. Now it's spit in the ocean... SFC mods and models didn't help... and I'd get either SATA (ATA 150) or ATA 133 all spinning at least 7200 rpm.
As to CDROM, DVDROM, etc., it's all personal needs, including things like maybe a Zip drive or these great new li'l inventions, flash drives.
And very importantly, get a GOOD power supply; at least 400 W from a reputable company, as if it fails, it just might take your mobo and CPU with it, like Khan tried to do to the Kirk gang. Make sure that +12 V rail on the supply is at least 15 A so it's stable.
Monitor? Hard one. Even 19" CRTs are quite affordable, really, but even only 15" LCDs are quite expensive. Suit yourself.
Oh, as for the case, I'd say unless you're a li'l kid and want to wow your buds, get a cheaper metal one with either lots of fans or cutouts for lots of fans. But be sure to put in at the minimum two case fans, three if you can fit them. This is especially if you get these new Athlon 64s from AMD or the newer Intel Pentium 4s. They ALL run hot. Did I mention the heat?