Atmega-328 as an alternative to the Arduino Uno
This setup only for running uploaded program. Not included voltage regulator, USB to Serial part and many component. Atleast, I recomment to design Serial port to debug or re-upload the program.
Also, You can use Arduino promini schematic as reference which include power led, d13 led, some circuit for upload code with usb to serial and reset button. I have done many custom PCB based on Arduino. these component will help ypu develope and debug quit easily.
Depend on you IO, if you want very small circuit with less IO you can try Digispark Attiny85 Arduino competible.