best way to power arduino

i am building a sumo bot. for this i am using an arduino uno rev3 board, grove sensor shield, two 12v 1.5A motors and i want to use an arduino motor shield. from all the documentation that i read if using a 12V battery it is recommended to cut the "Vin Connect" jumper because 12V is too much for the arduino board.

in this scenario what is the best way to power the board?

the two options i can think of are: 1: run the 12V power directly to the motor shield. install a 9V regulator parallel to the battery and using a 2.1mm center-positive plug connect it to the board. (is this too complicated of a solution?)

2: run the 12V power directly to the motor shield. install a 5V regulator parallel to the battery and send the 5V and Ground to one of the unused connectors of the sensor shield. (would back feeding the board this way fry anything? or would it cause problems with programming it if the external power is still hooked up?)

It will run hot at 12V, but this should work if you don't pull much extra current from the 5V rail.

It is nice to isolate the Arduino from fluctuations on the motor supply though, the extra 9V regulator (if it has a generous decoupling capacitor on the output, say 470uF) provides this.

Using a DC-DC converter to take 12V to 5V is another option - frequently these devices have a wide input voltage range so will cope with 12V fluctations - they are also more efficient than a linear regulator.

i will have five parallax ultrasonic ping sensors on the 5v rail. the data sheet rates them at 35mA max for a max total of 175mA. (altho i'm not sure how much current it takes to command the motor shield)

I don't see anything wrong with using a 7812 (variable voltage regulator) and dropping to ~ 8V using some sort of resistance to the center pin. It can do about 750mA, which is more than enough for the arduino.