What is the minimum parts needed for a standalone project?
I'm thinking the chip and a crystal.
Anything else?
You also need the two small capacitors.
Not strictly needed but smart to have is the reset button and the pullup resistor.
Which two caps? The one between +5v and gnd & aref and gnd?
Which pull up resistor?
There are two saml caps connected to the crystal i think they are 22pF but my memory may fail me here.
The resistor i mentioned is on the reset pin, i cant remember if its pulled high or low (i.e. goes to +5v or ground)
The simplest practical circuit is probably that used by the RBBB:
http://shop.moderndevice.com/products/rbbb-kit
I've built several on bits of stripboard.
If you use a creamic resonator in stead of the crystal (like the RBBB does) you don't need the two small capacitors.
Take a look at my Perfboard Standalone and you ll have the clearest idea of minimums for full functionality.
http://www.musheen.com/perfboard-standalone-arduino-ii-691.html