I would start with the Eagle schematic and PCB from the Arduino Diecimila, or Arduino Single-Sided Serial Board (version 3)
An Arduino UNO, has a lot of circuitry that you do not seem to need.
The Diecimila is less complex than more recent Arduino's, which have smart power selection, and a different USB to serial interface.
I assume you can use Eagle.
I assume you do not need the USB adapter on board. I'd buy one ready made from eBay for a few $'s instead.
Arduino Single-Sided Serial Board (version 3):
Load the schematic and PCB into Eagle
Delete everything to the left of JP4, labelled 'autoreset', including JP4
Delete J1, J2, J3 and power header
You have a schematic which does everything you have asked for, and a PCB ready laid out.
Diecimila (more to delete):
Delete the FTDI chip, and all the parts out to and including the USB socket.
Delete the Tx/Rx LEDs and resistors, the FTDI chip has gone, so there is nothing connected to them.
Delete the 3-pin header which chooses power from the external socket or USB.
Either use the 2.5mm barrel jack to connect your 9V battery, or delete it, and replace it with a battery lead (a two pin header will do), and connect it to the connection remaining after deleting the 3-pin power-select header.
Delete the Arduino 6 and 8 pin header sockets.
Now, you are pretty close to a Diecimila-based schematic, and you have a much of a PCB layout if you want to use SMD parts.
If you do want to use the Arduino PCB layout as a starting point, adjust the board dimensions, and carefully select and copy the parts and tracks to a convenient location.