Just had my distributor rebuilt and they said to oil it after I put it on the car. It has a little lid you flip open and add oil. How much and what kind should I use?

Use the same oil that you put in the engine. Flip the lid and fill. This oil will leak back in to the engine. Don't forget to add a few drops of oil to the felt pad under the rotor. Too much and it will fling out and on to your points then leak down and out on to the intake.Do this each time when you change you oil.