As PC eye said, Vista is able to operate on a wide variety of platforms. However, here are a couple things to keep in mind:
Running it on an older 3.2Ghz Pentium 4 Prescott personally, I found it to be taxing slightly. It wasn't slow, but it wasn't fast, either. Some processes took a bit of time to come through. Really, with the low cost of dual core processing, going with a cheap Athlon X2 CPU for the most budget-minded or a Core 2 Duo processor for somebody with a bit more cash to spend would be optimal. Motherboard is solely based on the features you need, whether you want to overclock/tune your stuff at any point, interconnectivity/in-out ports, etc. Spending a little more on the motherboard is always good! I regret my motherboard purchase very much!
Graphics are a big debate for people. Honestly, DX10 budget cards are on the way (don't know if they are out yet). If you don't do alot of gaming, there will be an 8300 [?] nVidia card released for less then 100 dollars, if you play a few games then the 8600/8600 Ultra [?] will suffice - and if you plan on doing some extreme gaming or want to enjoy the in-development blockbusters that are on the way [ Microsoft: Crysis will be the Halo 2 of Vista] then an 8800 GTS/GTX would be good. However, wait until A-The ATI R600 GPU drops to bring competition and B - nVidia ships a DX10 driver. No reason to buy a DX10 gpu before the driver is ready. And since you aren't probably anxious to buy it all before this weekend, you can wait a little bit longer. Now is a VERY exciting time for computers. Vista + DX10 + Quad-core is crazy right now.
The other components are up to you. If you want maximum speed, you could get a Raptor high-rpm hard disk to put your OS on, and a larger lumbering 320+ GB hard disk for data storage, or just one large 500GB - whatever you really like. Sound, keyboard/mouse, case, optical drives, etc are all your personal preference.
The last thing I will say is this: In considering a new computer, spend the money for a good display. Having bought my 20.1" Dell monitor, I am VERY happy now. Before, not so much. Spend the money on a decent display. Lets put it this way, a computer case is likely to have its internal components replaced once or twice between monitor upgrades/purchases. Therefore, spending money on a monitor now means you will be satisfied for years to come, rather then buying the bare minimum of your wants. I would recommend shooting for larger then 19" for space and size. Also, keep in mind HDCP - this is the standard which requires a protected output, connection, and display device in order to play protected HD content. So, if spending the big money for a display, keep your eyes open for a HDCP display. You'll be mad if you buy a good graphics card and later go to play an HD movie on yoru new HD-DVD ROM in your computer and you can't watch it at full quality because of DRM down-sampling.
Remember, this is just one person's opinion. These are just some things to keep in mind!

Happy shopping, there are lots of folks to help you out along the way. Just keep in mind there is alot of personal opinion running around, it is up to YOU to decide what to believe and choose.