First, decide if you want a laptop or a desktop machine. When deciding this, remember that laptops are more expensive to buy, more expensive to repair, and more expensive to operate (batteries cost big bucks). Also, keep in mind that while people generally buy laptops for the mobility convenience, few people actually use them for that capability. Most of the time, buying a desktop machine is the best option.
Second, are you getting a Windows or Macintosh machine? I view this choice as simple. Around the world the vast majority of machines run Windows. There are more software choices available for Windows and it is MUCH cheaper to buy both hardware and software for Windows than Mac. It used to be that Mac was better for graphics and sound, but so many improvements have been made in these areas on the Windows platform that I can no longer see any reason why choosing the Mac is a good idea.
Next, what are you going to do with your machine? School Reports? Database work? Graphics Design? Movie Editing? Gaming? Maybe just browsing the web? Each of these would have slightly different hardware configurations.
Basic Configuration
PROCESSOR: My personal opinion here is to stick with Intel chips. If you are squeezed for cash, the Pentium D chips are a great value. If you can afford it, go with a Core 2 Duo or Quad. These are either dual or quad core processors with tons of power! Price obviously goes up with speed, but the price will increase faster as your processor speed increases, so if you can stand a slower one, it will be cheaper.
MEMORY: 1 GB minimum, but buy as much as you can afford. The more you have, the faster your computer will seem to run. While you can get away with the 1 GB, I wouldn't buy a computer with less than 2 GB today.
HARD DRIVE: get at least 120 GB, but don't waste your money on the new Terabyte drives. If you use up your original 120 GB, it is cheap and easy to add a second hard drive.
MONITOR: Get at least a 17" screen. LCD Flat Panel displays are great if you can afford them because they take up less space than standard CRT displays, give off less heat, and are generally easier on the eyes. If you must get a standard CRT screen, get a Trinitron monitor as they are much easier on the eyes.
GRAPHICS CARD: Get at least a 128 MB graphics card. If possible, get a 512 MB card. The cards made by nVidia (geForce) and ATI's Radion and Rage cards are very good. If you are going to do gaming, bump this up as high as you can afford.
SOUND CARD: I highly recommend Turtle Beach cards, but SoundBlaster cards are also a good choice. If building your own machine, the onboard sound with the motherboard is usually sufficient.
MOUSE: Always get an optical or laser mouse! They are always accurate and you never have to clean them out. I love my Logitech mice. I use the MX610 regularly. This is a cordless laser mouse. The batteries tend to last a couple of weeks. I use rechargables so it doesn't cost much. These new mice also have lots of buttons. Don't buy one unless it has a forward/back button for the web. My mouse also has volume controls on it, which has proven really convenient.
OTHER DRIVES: If you have a choice about getting a floppy drive, don't. There really isn't much need for a floppy since Windows XP and Vista allow for bootable CDs. I do highly recommend a DVD-RW drive and a DVD drive. These should be the fastest you can get and it would also be acceptable for a combo drive.
SCANNERS/PRINTERS: I highly recommend Epson inkjet printers because they offer finer ink droplets, fast print speeds, and affordable supplies. Even the most inexpensive Epson printers are far better than most models offered by the competition. For laser printers, I have had excellent luck with my Samsung CLP-510n color laser printer. For scanners, go with HP. The HP scanners are fast and accurate, giving brilliant colors and specacular copies. The newer models even scan 3-D objects just like a taking a picture!
WHAT BRAND? I personally recommend Gateway. They offer great hardware options and reliable and helpful support. If you don't care about getting a custom built laptop, Toshiba and Sony are both very highly rated - they just can't be custom configured. I have purchased several refurbished Gateway machines for others and all have fallen in love with them. They haven't experienced any trouble so far.