Now...to the system itself. There are a number of nettop options. But you might be better off building your own mITX system. It will probably be a little bigger, but you will get more bang or the buck.
If you want the absolutely smallest case you can find, you could go with the M350
. You can also get it with various power bricks. This model
has a 150W power brick. You could also go with the In Win BP665
or Antec ISK 300
There is a range of prices there for the case from about $50-100.
Then you would need an mITX motherboard like this ASRock board
for $100. If you go with this 8GB kit
A 1 TB WD 7200 RPM drive
Just for pure longevity of the system, I'd recommend an Ivy Bridge i5. It pushes the power budget on those cases a bit being a 77W rated process, but the [utl=http://www.newegg.com/Product/Product.aspx?Item=N82E16819116504]i5-3570K[/url] does have the HD4000 graphics that really are a huge upgrade for Intel integrated graphics. That processor is $230 unless you have a Microcenter
That's a very potent system for under $500 if you use the InWin case.
Now, that said, it is also overkill in the extreme for an internet machine. You can get by with an i3 or even one of the AMD options. The AMD options are less power efficient, but give much better integrated graphics. And graphics performance can be a factor in system longevity. Of course, any of the boards would support an add-in video card to extend system life, though the cases and power supplies that I have mentioned above would not.
I you have a Microcenter near you, you can get the i5-3570K and ASRock Z77E for an amazing combo price of $275. Unfortunately, they don't really have any mITX cases. But you can always order a case online. With that sort of head start, you can even cram in a small SSD boot drive if you like.