You would be best served to just buy a laptop.
My advice is get an HP, Asus or Toshiba 15.6" laptop with the A6 series AMD APU, 4GB RAM, Windows 7 64bit.
You can then ADD a separate monitor. If possible, get a quality 22" 1920x1080 screen.
*Some monitors have an HDMI input and speakers. If these are adequate you can do something like this:
- hookup LAPTOP to screen via HDMI (change audio device to HDMI)
- use Logitech Mouse/Keyboard with micro-USB adapter
- Move laptop to a convenient spot since you don't need its screen or keyboard.
The APU fan is incredibly quiet as well, basically silent. I've seen very nice laptops for only $500.