You can use potentiometer inputs, but it would be simpler and cheaper to use some other type of input to set the timers. Timers can be set using a thumbwheel input that can use 1, 2, 3, or more "digits" to input a number from 0 to 9 (1 digit), 0 to 99 (2 digits, and so on. In your case you could use two 2-digit switches to set the 20 to 60 second timer, and the 0 to 10 second timer.
To use pot inputs, you will have to feed the pot voltage to an analog input, then convert it to the number range of your Click timers. Looking at the Click I/O, due to the limited number of Inputs, it will be more efficient to use one of the 3 models that have analog inputs (C0-02DD1-D, C0-02DD2-D, C0-02DR-D). The C0-02DR-D has relay outputs and the other 2 have transistor outputs.
If you are going to need more than 4 digital on/off inputs, then I would buy the C0-00DD2-D $69 CPU, and a 16-input C0-16ND3 add-on input module for $45 (instead of an analog CPU for $129). That would give you enough inputs (4 for 0-10, 6 for 0-60) to use thumbwheel switch inputs instead of the pot inputs.
Once you decide on which method and which Click modules you will be using, then the ladder logic program will be fairly easy.