Will the Mac Mini drive 2 different displays I want to switch my windows machine with a mac mini.  I have 2 monitors:
A VGA driven display
A DVI driven display

My pc graphics card can handle these outputs.

The Mac-Mini has a HDMI display and a thunderbolt display.

Would I be able to get a converter that would drive:
The HDMI to DVI?
The Thunderbolt to VGA?

I'm already spending £700 on the mini, I don't want to spend an extra 300 on monitors
Yes it will, exactly in that configuration. 

HDMI to DVI you can use any cheap converter it does not matter. Mini Displayport (aka Thunderbolt) to VGA i suggest buying an apple branded converter, i've had trouble with third party ones.
You can probably get both, apple branded for cheap from ebay as long as you make sure they are in good condition.