It is just that, to me, the description sound like just a couple of inputs and outputs, for which a full blown PLC is slightly overkill.
My personal alternative to a PLC, apart from hard wired, would be a small Picmicro, 8pin/12pin, whatever method, other I/O hardware is required.

 

Which ever solution is used, the voltage and current requirements of the motor and solenoid are needed to complete the design. I would chose a ATTiny-85 8-pin micrcontroller to run the program sequence, only because I am very familiar with the Arduino compatible devices. The motor and solenoid will require driver transistors suitable for the load requirements and the power supply will also be dependent on the same. It would be a very simple circuit, with all the smarts being taken care of by a very simple program.