1) Obviously Sound card and Monitors are most important. Beyond that it depends on the type of task. Softsynths will be typically be CPU limited, Multitrack recording Harddrive IO limited. I would perhaps look at this page for Ardour http://ardour.org/linux_system_requirements which basically says that any modern hardware will be fine.

2) Dual core should be fine, Quad cores will allow you to run more tasks at once. Currently it seems that intel have best low power options with the i3,i5,i7 series. AMD might be worth a lookin if you also want accerated graphics on a budget.

3) I built a system with the Antec P180 case about a 2 years ago. It worked quite well. There may be better options now.

4) Because I have a firewire based audio interface I have been going with Gigabyte Mainboards (TI firewire onboard).

5) Whatever you find a comfortable size to use. I have a 23 " in front of me at the moment and it seems a pretty good size to work with. If you also do a lot of photography or graphic design then I would look at either an IPIS or PVA based monitor IPIS monitors typically start at 1000 dollars.

6) Fans will largely depend on what else you end up doing. Larger fans typically make less noise.