I am seriously considering the possibility of a Ubuntu 8.04.1 based machine for the following reasons.
security - viruses, malware, the lot I am running a McCafee - however it is spelled
speed
free
64bit

I know that the 780G AMD chipset by far offers the best graphics for a integrated mobo. However, I wonder if it is worth it to build an AMD based machine based upon this if the majority of my uses will be CPU bound.
ie. I won't be gaming on the thing.
The only other choice seems to be intel with intel integrated graphics, which quite frankly are terrible. However, their CPU's are much, much faster.

The uses:
media player- full length movies, music etc.
media encoding & converting
school projects
casual web surfing

budget:
CPU - $100 - 150
Mobo - $< 100

If you have ne questions ask. thanks.

I think that for your uses, an AMD machine will be the best bang for buck, and should work excellently.

If you're planning on overclocking the 780G may not be the best idea as many of those chipsets have power issues (see all the griping at Anandtech). There are supposed to be new revisions of some 780G boards with better power regulation to enable use of AMDs higher wattage CPUs, but I don't know if those are out yet, or if they really addressed the problem.

That said, for no overclocking, the following would be pretty decent:
mobo: http://www.newegg.com/Product/Prod [...] 6813128090
cpu: http://www.newegg.com/Product/Prod [...] 6819103234

If you needed a graphics boost, you could toss in an HD 3450 and enable the hybrid graphics.

For media encoding, (particularly HD movies) it would be nice to step up to a quad-core CPU. I think AMD should be lowering its quad and tri-core processor prices soon, so you may be in luck.

Anandtech thinks the 9550 should be priced at around $175 (http://www.anandtech.com/cpuchipsets/showdoc.aspx?i=3344), so if you could step up to that, you'd see a pretty big boost for HD video encoding, otherwise, the higher clockspeed of the dual core will likely win out on audio encoding/converting.

If OC'ing go with the 5000+BE, if not this one should fit the bill nicely: http://www.newegg.com/Product/Prod [...] 6819103255
($83)
or go with a tri-core: http://www.newegg.com/Product/Prod [...] 6819103254
($149, can't OC much, if at all, but should work nicely)

as for MB: http://www.newegg.com/Product/Prod [...] 6813131318
($83, also has an eSATA port, remember if using an AM2 proc to get DDR2 800)(if using the tri-core, get DDR2 1066)

for a Vid card: http://www.newegg.com/Product/Prod [...] 6814102152
($58 for now)(have a bunch at work, no issues with em, other than a few DOA's but after ordering about 70 of em, we got maybe 5 DOA's)

You could run Ubuntu on some pretty old machines and still get great response, speed, etc.

If you're looking to save money, then yes, the AMD 7x0 series will be your best bet as you get awesome IGP and on Linux you probably won't notice that much a difference between AMD/Intel chips in terms of speed.

The mobo zipz0p posted is good, but for a CPU, I'd try and get a cheaper AthlonX2. This seems to be the best one I can find. Anything below it I think is Open Box or no HSF.

http://www.newegg.com/Product/Prod [...] 6819103064

So yeah, it's 500 MHz below the one zipz0p posted, but you most likely won't notice that much of a difference and you can probably OC it anyway.

I concur with other posters Any of these options will be mighty snappy on Ubuntu.

I wouldn't recommend an ATI card for Ubuntu at this time Google it and you'll understand.
And yes I know ATI has recently opened up it's drivers, but it'll take awhile. Running a dual boot of XP and Xubuntu here, You should really look into building a Xubuntu machine if you want some real speed.

http://en.wikipedia.org/wiki/Xubuntu

It looks like AMD has improved the Radeon linux drivers immensely. Also looks like EnvyNG should work pretty well with Hardy Heron (8.04), though I haven't tested this myself - I probably will with my old P4 + 9800Pro in the next month or so.