Pushbutton differences are very slim between the four models, with the exepction of the late A906.
The 160, A900, A902, and early A906 all have the exact same timer and water level controls. The cycle times and programs are identical between the four models.
The later A906 used a dual motor Kingston rapid advance timer, and a dual diaphragm pressure switch. The cycle times are slightly longer due to the escapement differences.
The lid switch and unbalance methods changed throughout the build. Early 160's use an unbalance switch integrated into the lid switch. Later they removed the trip style unbalance switch and went to heavy duty cork pads attached to the base plate such that the brake would drag and keep the speed slow (late 160 and A900). By the A902 they went back to a solenoid kick-out switch style where a trip lever is attached to a mag solenoid on the outer cabinet, much like a Kenmore.
By the revised control (late) A906, they went to a standard style out of balance switch much like that of the revised switches on the A806 after 1967.
More detail can be found at the end of the service lit.
You should be okay and have the early design considering you have a February 1960 machine.
Ben