sounds like a fun starter project!
Well for your purposes, i think the 328 should suffice.
What you made is all quite simple if you just go through the playground a bit and find what your looking for.
As for the pir, theres some sample code here;
http://www.arduino.cc/playground/Code/PIRsense
The lcd screen:
and the info to use it:
http://www.arduino.cc/playground/Code/SLCD
and for the buzzer, either find a 5vdc buzzer, or perhaps use a relay with a louder buzzer, connected to an outside power source.
GOOD LUCK! and please keep us updated!