The choice of motor will depend on the overall weight of the trike (trike + battery + payload).
You mention only forward and backward (as opposed to turning), but do you have a specific speed in mind?
An easy way would be to have a motor connected to a rubber wheel which presses against the main wheel. The speed is slower, but can be easy to do and no additional sprockets required.
If the weight is not too high, a power window motor should do the job.