I am not a Linux expert. Far from it.
Best bet for CPU would be retail box, and use the cooler that came with it. Guaranteed to fit the MicroFly. The Abit board has Smart Fan. Just enable it in BIOS and it will run the fan slow, and will automagically speed it up only when needed. Under these conditions it's amazing how quiet a retail box AMD fan can be.
Everyone has great suggestions, but...
	
	
		
		
			I hope to keep it CHEAP.... 
I got this system a long time ago .... It's an AMD CPU. I have 256 megs of RAM... not enough hard drive space ...
		
		
	 
I think the cheapie system I recommended fits the bill... cheap, quiet, fast. Are there cheaper? Yes. Are there quieter? Yes. Are there faster? Definately yes. Are there all three? Haven't seen such a suggestion from anyone else yet.
The thing is that what I suggested is not the best choice for any particular reason. However, I believe it to be the best choice based on a particular 
combination of reasons. Additionally, I believe it will meet and exceed cindyhot's expectations 
in comparison to her existing system.
Yes, a stock speed $300 Core 2 Duo E6600 will rape the highest overclocked Sempron in any benchmark. However, her basis for comparison is a several-year-old AMD. A socket AM2 Sempron will already be much better, plus much friendlier on the pocketbook.
Zebo is right in saying that all HDDs vibrate. However, a modern HDD with fluid bearings (basically they all are these days) will already be quieter than a 100GB HDD from several years ago.
Yes, there are really "quiet" power supplies when compared to the stock Ultra V-Series. However, it is probably going to be a lot quieter than any PSU from several years ago when nobody paid any attention to these matters over their 6800RPM Delta 60mm fans.
My point is this: I think everyone is trying to oversell her. I know everyone has the best of intentions. Yes, this part is quieter. Yes, that part is faster. What it comes down to though is balance and relativity. A balance between price, performance and quietness. Relative to her current/old system, noticeably faster and quieter.
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How about an analogy? She's coming from a 20 year old Ford Escort that's slowly becoming a rattling deathtrap. Wants something cheap but is "nicer" than that old beater. One person recommends a Corvette, because you can never get enough performance. Another person recommends a Mercedes, because it has style and is really quiet inside. Someone else recommends a Hummer because you may one day have to transport a number of people.
I'm the one trying to recommend the Honda Accord. It's sensible, cheaper than the other recommendations and it exceeds the car it will be replacing in all ways.