I would like to install a receptacle under the sink to control the dishwasher and garbage disposal, with a single pole single throw switch mounted in the wall above the counter top to control the garbage disposal. In the load center I would like to use a 20 amp GFCI breaker to power the circuit. I'm using #12/3 romex to feed the circuit. My question is, would it be better for me to replace the garbage disposal with a unit that has an automatic sensor that activates the disposal when the plug is inserted or turned rather than going to all the trouble of mounting a switch on the wall. Since the dishwasher and disposal don't run at the same time and the full load amps are less than 14 amps on either appliance, I'm thinking I can just use a 20 amp GFCI receptacle and save on the GFCI breaker. I would really like a professional opinion on which way proceed.
It is not permissible under any electrical code to assume the dishwasher and disposal won't be used at the same time. If they can be used at the same time, you must design for that condition. For the United States:
Beyond that it's better to either hard-wire both appliances, or provide two GFCI plug positions. The code gets more complex for mixed setups. See also the answer at Can I split the direct wire to dishwasher to handle a garbage disposal as well?
If you're using 12/3 with ground, non-metallic sheathed cable from the panel to the outlet, you'll have no problem doing what you want.
Pull the cable
Install the switch
Install the receptacle
Install the breaker
Turn on and test the GFCI breaker
If the breaker will not switch on, there is a ground-fault, the wiring is wrong, or the breaker is bad. Detect and correct the fault, and reset the breaker.
Here is an image showing what the finished circuit should look like.