how to power the ATMEGA328P-PU

Look at the Promini instead

That's a pretty minimal set of components.
If you use the internal 8MHz oscillator can get by with even less at some reduction in speed accuracy for timed events (browse the forum for discussions on that).
This site has a clone with all the components mounted right on the chip itself! And have seen pics where others have done this without the board. So you don't many parts.
http://www.solarbotics.com/products/kardw
huh - they even have a link to it
http://www.geocities.jp/arduino_diecimila/obaka/project-2/index_en.html

I was playing around with doing the same thing with a '644 chip, more memory, more I/O, 2 serial ports. Would also fit on the 1284 which has 4 serial ports.
http://www.arduino.cc/cgi-bin/yabb2/YaBB.pl?num=1289437587/all