To me the engine is one of the most important things when I am trying to get someone to buy my car. Engine performance can be one of the biggest factors when a buyer wants to buy my car. Things to consider are whether the engine turns over easily, does the engine conk out unexpectedly and how well the engine runs when stationary (how well it idles). Buyers have an uncanny sense of whether or not the car has an adequate engine. You should also be prepared for the buyer bringing along a friend that knows a thing or two about the car. There are more things than this to consider when I attempt to get someone to buy my car.
Other things worth considering are whether or not the engine warning lights work then making sure none of them are lighting up when you start the car. This early warning to the buyer coupled with a noticeable problem such as the idle speed seeming high or too low can be a warning sign of something mechanically unsound with the vehicle. This is why I think it is important for the car to be looked at by a mechanic before I want someone to buy my car. A lot of buyers will actually take the car to check it out at their own mechanic when they want to buy a car. There is nothing wrong with this; you can't blame the buyer for exercising some caution before handing over money for a car. This is particularly important if the car is an upmarket model where repairs may be quite excessive.
If the engine is not performing at its peak proficiency then there may only be something minor wrong with the engine. It is probably something that can be repaired by getting the car retuned or a loose accelerator cable. It is not the end of the world if the car is not running perfectly. A lot of the time something that seems like a major flaw may just require a simple turn of a screw to repair. Besides the engine the car may have some pretty good selling points. If the engine is beyond repair then talk up other advantages of the car. There may be someone in the market for something they want to repair.