I'm running Debian 6.0 on my main system. I have a test system/backup Dual Core Atom mini-itx running dual boot with Arch Linux amd64 OpenBSD current amd64. I have a very old laptop running Debian 6.0 and dual booting OpenBSD i386. and a newer laptop running Debian 6.0 dual booting with WinXP. I have another system with an all-in-one mobo that I put FreeBSD 8.2 on and tried the enlightenment desktop (enlightenment e17 was not very stable) I will probably try Arch with the new gnome 3.0 on the all-in-one mobo.
Some of these systems I have been able to put together for $170 but I watch for deals, put them together myself and shy away from high power bleeding edge hardware. In my opinion the best bang for the buck are the all in one mobos with embeded cpu (I bought an Asus C3 Terminator system for $45 that happily ran Slackware with an xfce4 desktop). Again, that was 45 dollar for a case, powersupply and all-in-one mobo. I added a recertified hard drive and dvd burner for another 50.
Biostar has a $62 mobo with embeded cpu and openchrome graphics that will run what you have mentioned but it will not be lightening fast or run flightgear flight simulator. It is enough for the base systems you are talking about.
If you want a higher end system I think Directron bundles together systems at a decent price. Link here:
http://www.directron.com/ho.html?_s_icmp=systemsale. I have had good luck with them but your mileage may vary.
If your are going to put something together yourself (It is really pretty easy) Newegg has alot of refurbished and openbox parts. This openbox system will run the default Mint, PC-BSD installs along with winxp but the graphics will not give smooth 3D accelleration needed by games:
http://www.newegg.com/Product/Produc...2E16856115035R
I was replying to your previous similiar thread but found it a little hard to make suggestions as I am not sure if you are going to do any cpu intensive processing. To be honest most of the systems you want to run have the same applications. Gimp will run the same in PC-BSD or Mint
If you want the latest and greatest applications at the expense of stability run Arch
If you want applications that have been tested and patched with an eye to stability try Debian or Slackware.
If you want to learn Unix as opposed to Linux try OpenBSD or FreeBSD. You will learn very little with PC-BSD.
If you want to get some idea how the linux operating system works try Slackware. You will learn very little with Mint other than which package in synaptic to click on.
As far as hardware, unless you are planning to run multiple, threaded applications concurrently, you will probably not see much difference between a dual core and a quad-core cpu.