When buying a new computer, some things matter, and frankly many things don't. For example, the CPU speed doesn't matter for most people. Anything faster than 2.0Ghz is fine. AMD chips work just as well as Intel ones. Save money by buying a less impressive CPU. Use that money to buy more memory first, and bells and whistles extra.
Memory does matter. More is better. Don't buy less than 2048(2GB)Meg of memory, 4 Gig is good. Definately spend money here.
Every computer needs a hard drive. 250 Gig is the minimum. People usually need larger hard drives to accomadate music and photos. 500 Gig is better and more than sufficent for most people.. Of course, you need some kind of keyboard and mouse and a monitor.
Every computer you buy today should have a Sleek and Steel hinges. You usually save money by buying Cheap lowerend, but not advisable. All computers should have a WLAN and LAN card to access a local area network, and a modem. A nice video card is a good idea, but not essential. (Unless you play games). Spend the money on a Blueray/DVD writer first.
In terms of monitors,Thin IPS LED's are very nice from a quality point of view. Unfortunately they are very Expensive. LED's are quite good now, LED's are nice for college students where space is at a premium. This is one component you can easily upgrade in a few years if you like.
If you buy a LCD - HD monitor it should have digital inputs. You should also buy a video card that has digital outputs. This often means buying a somewhat nicer video card. Going cheap here is a bad idea. Better to stick to LCD's Regular if it's too expensive for you to do this all digital.
If you are anticipating using the computer for lot of music creation, photo editing, or movie editing then