Intel's Core 2 Duo chips are faster due to architectural improvements, for the most part, not so much from being dual core, which is why they spank Pentium Ds (also dual core). The Pentium 4/D series was designed to achieve huge clock speeds, but they don't actually get much done in each cycle. Core Duos have lower speeds, but get more done per cycle, like AMDs chips do. They also have improvements such as 128-bit SSE, which AMD has yet to match (this is one of the sources of Intel's current performance edge).
On the subject of PSUs, it is very rarely worthwhile to buy a cheapie. The PSU is actually one of the most important parts of your machine, and buying a poor one can lead to instability, shorter component lifetime, and potential early failure (and in the case of cheap ones, they don't often have the extra features to prevent them from taking your other parts with them when they go).
Most generally, included-with-case PSUs are cheapies, and are not to be trusted with any sort of demanding or costly components. Save up a little more cash and buy one separately.
In looking for a PSU, always closely check that is has strong amperage on the 12v rail(s), as this is the most-used voltage in modern systems. A good PSU should have very little discrepancy between the actual voltages, and the levels they should be, and should stay solidly there rather than bouncing around. Overvoltage and short protection are also very good things to have.
You can't generally tell online, but there's also a positive correlation between weight and quality of a PSU. Heavier models are generally made with more robust transformers, which is always a good thing.
AGH I DONT SPEAK LATIN!!!

(admits patheticness)1
I just wish somebody could put things out simply. what would be a good set of parts I could get for around 800$? (I thank you multi and others, but I want more than 1 recommendation, preferable kryo would be a nice source)
Comparing the Pentium D with the Dual core duo. is like comparing your 7 year old pc with my 4year old one
oh thanks...
ok so I understand which rules, but I still need to know about other parts...
and its not exactly like my wallet is of infinite depth...
better yet, kryo... buy me a computer and place it in for tax deduction as a buisness expense (a design consultant, i.e. I play the beta) and I'll pay you back