seemingly easier to work with common cathode LEDs.
I can''t see why one is easer to use than the other, you are just sourcing current or sinking current, it's just the same.
Can I power the Arduino with 12v via the input jack
Yes
and have the positive end of the LEDs attached to Vin
Yes
and the negative end of the LEDs attached to the pwm pins
No because the maximum voltage you can apply to an arduino pin is 0.5v ABOVE the supply voltage which is 5V because the regulator cuts the 12V down to 5v before it reaches the arduino.