What machine to get depends on what you want the machine to do and how much you want to spend. Its generally a pretty good idea to look for a machine you can "grow into", as opposed to one which meets just your immediate needs.
As minimum considerations, I'd look for a relatively fast (1.5 Ghz or greater) processor, at least 512MB of RAM, a 30GB or larger hard drive, a 14" or larger screen, a current operating system (such as Windows XP Home or Pro, Media Center, Tablet, or Server, all with SP2, or Mac OS 10, if you're looking for a Mac), USB 2.0 support, Ethernet and/or Wireless Networking support, an onboard write-capable optical drive (ie; CD-R/RW, CD-R/RW-DVD or DVD±R/RW), rated battery life of 3 hours or greater, and at least 90 days of 100% warranty, with a full year to be preferred. If graphics or gaming are important considerations, the machine's display adapter will be critical; you'll want a relatively higher-end, hardware-type video adapter with lots - 128MB or more - of its own memory. If gaming/graphics aren't a big deal, you can save money going with an embedded/shared memory display solution as opposed to a hardware solution.
Good values may be found in the form of refurbished machines and/or close-out/discontinued machines as offered on the web pages of the various major vendors.
CNet offers a decent Comparison-and-Review website, as does
PCWorld, and many similar Compare-and-Review sites are out there on the net. The more research you do, the more well-informed, and likely happier, you're gonna be.
If you do decide to go with a used machine, be certain you have some recourse in the event the machine you get is faulty on receipt or otherwise not as represented/expected.
Its always a good idea to use an actual credit card, not a check or debit card, when making an online purchase; that way, should there be a problem with the product, you can contest the charge with your card provider - any other form of payment pretty much is gone when accepted, whatever else may happen.
Finally, I'll re-emphasize that you should get a machine that is capable of, or at least economically and conveniently upgradeable to, considerably more than your immediate current needs.