The title of this thread is self explanatory. here is some relevant information.

1. The desktop would be used primarily by my wife and my younger son who will be in 8th grade next year.
2. Majority of tasks performed be typical home and school work use such as surfing, e-mailing, some gaming (he does have PS2 and Xbox), writing school papers and reports plus managing music and video downloads (by my 12 yr old son).
3. bandwidth of my ISP is a bottleneck as my d/l speed is just over 1 Mbps and u/l speed is about 350 kbps.
4. I am thinking that the PC should serv etheir needs for the next 3-4 years, although my son's usage pattern and his needs, as well as evolution of technology provided in mainstream home PCs will change during the course of the next 3-4 years.
5. The most cpu intensive task that my son does is processing music and videos to transfer them to his iPod.
6. He is not into heavy gaming on PC but he will play some games.

I am not a computer expert, but I understand some basic things, maybe even superficially.
I know that in general, it's better to have more memory and slower CPU than a very fast CPU and not enough memory.
The main issue is how to balance or match CPU and memory.
I am willing to consider refurbished models.
I am unable to decide among three following types of processors
AMD Athelon II X2 processors
AMD Phenom X4 processors
and AMD Phenom II X4 processors.
I would like hard drive size between 500GB and 1TB
I would like either the amount of memory that makes the most sense for a given processor given the scope of the tasks I described. The route of getting the least memory and then upgrading yoruself does not often work as you ened up throwing away some of the memory that came with the system. For example, upgrading from 4GB (4x1GB) to 8GB (4x2GB).

I understand this covers a wide range of processors, partly because I know little about capabilities of various classes of processors and partly because I am swayed by comments I have read on lots of sites from people who may or may not know much themselves. Several people here are very well informed about these issues and I have far more confidence in their advice than what I read on the internet.
As an example of systems I have looked at are
HP Pavillion p6320 HP Pavillion p6320 : Phenom II Quad Core 2.8GHz CPU, 8GB RAM, 1TB HD
HP Pavillion s5310y AMD Athlon™ II X2 250 3.0 GHz, 4 GB DDR3, PC 8500, 640 GB HD
My range is roughly from $350 to $500 plus or minus 10%
There are so many variables, the motherboard, the FSB speed, the memory speed, the vido card, that I get lost.

Although this post is lengthy, I still might not have provided all all information you guys may need to help me.
The desktop they use currently is a Compaq SR1625NX with an Athlon 6400, 3200+ with 1GB of DDR RAM with a 160 GB HD. The DVD writer is ot working properly. It can write CD''s but does not write DVD's. I bought it in Dec. 2005. I have rarely used it myself. Given the cost of a motherboard, memory, an HD, and a DVD drive, it's probably best to buy a new PC.
I have a spare license for Microsoft office 2007 Home and Student edition and a Norton Internet Security, so I don't need to pay for these.

Thanks every one in advance.