It comes down to how technical you are. If you're not technical at all, I would suggest a Dell... but not a Dimension... get a Dell Optiplex. They're built to a higher standard, usually come with a 3 year on-site warranty and usally have better support.
If you're somewhat technical... defined as being able to install Windows yourself from scratch or install memory, then go with Logic Computer House or Canada Computers as Edifice mentioned.
Stay away from Windows Vista... it's not fully baked and won't be for at least another year. Get Windows XP if you want Windows and want something now. Or if you want to get into the Linux world, Ubuntu Linux is a very easy-to-install, easy-to-learn Linux distribution.
As for processors... AMD processors (Athlon X2) offer the best value for processors that cost less than $200. For over $200, the Intel Core Duo E6400 or higher is the way to go. In both cases, stay away from motherboards that use Via or SIS chipsets. Via is unreliable and SIS stuff has been orphaned because SIS has been bought out by nVidia which has their own competing products.
If all you do is web surfing, music and document stuff, then the graphics card doesn't matter. If you play graphically intensive games, then it would be worthwhile to get video card. One of the best deals for entry level gaming is a card with an NVidia 7600GS (goes for about $120). For around $150, you can get a 7600GT, for around $260 the ATI X1950XT is the way to go, $400 gets you an NVidia 8800GTS which can handle just about any game, and for all out performance and bragging rights, $900 will buy you the NVidia 8800GTX.
For sound, any onboard sound should do you fine... unless you're an audiophile... in which case get a Creative Labs X-FI card.
For RAM, get at least 1GB ram... 2GB if you have the money. Don't bother with high performance memory. It's only worthwhile if you plan on overclocking.
For hard disks, just stick with SATA and get at least 250GB.
For monitors, pick something you like that fits your budged and stick with reputable brands like Viewsonic or LG.
And finally, if you're getting a computer from Canada Computers or Logic, get a decent case that comes with a good power supply. If you want a tower case, an excellent choice would be the Antec Sonata. Antec in general makes good cases. For a small case, stuff made by Shuttle would be a good choice. Cheap cases with cheap power supplies can make a computer unreliable by causing instability and even destroying components.