Congratulations on your Corinthian. They are great little boats.
I use a little Evinrude 2 horse regular shaft outboard. You might need a long shaft for rougher waters. I use it in the well, and remove it, and stow it in the cabin floor when sailing. It's best to keep the motor as far right in the well as possible to avoid hitting the rudder when both are turned. I pin the motor well plug in place while sailing also, to keep from shipping water when heeled over on the starboard tack.
The 2 horse is fine for getting in and out of the harbor, but is a little underpowered for choppy seas. I normally keep the mainsail up if I need to motor any distance. I think a powerfull electric trolling motor would do ok also.
The Corinthian sails so well in light air, that a motor is not as important as with some boats. Do you have a good, light genoa?