Saying something is .40 caliber is not going to be definite enough to give you an exact recommendation. You have to actually measure the bore( land to land) and groove diameters to help in deciding which diameter ball to use. .40 caliber rifles used both .390" and .395" balls, commonly, but there are others who require balls of smaller or larger diameter. As for powder loads, generally start at the same amount of powder as the caliber if the barrel is( 40 grains of Goex FFFg powder). YOu can usually work up to 1.5 calibers in these small caliber guns ( ie. 60 grains of Goex FFFg powder) without causing any safety issues. If you have a longer barrel, you may even have to use more powder to keep crud from caking in the last few inches before the muzzle with each shot.
For short range shooting, plinking sessions, and even for hunting squirrels, you can reduce that powder charge down to 30 and even 20 grains, and still get amazing accuracy.