Using DC adaptor and USB cable as power supply ?

A common diode, like a 1N4001, would work. However, it will have a forward voltage drop of over 1 VDC so you'd have to deduct that from the actual voltage the Arduino (the actual drop will depend on current going through the diode, refer to the forward voltage drop vs. forward current graphs in the datasheets). A Schottky diode, like a 1N5819, also has a forward voltage drop but it would be much less, even at the higher current your motors would draw.