Look at the bendix end of that starter motor real carefully. There is a brass sleve bearing in the starter end plate. I have seen that bearing and end plate (aluminum) badly damaged from a starter and bendix that jumped on the worn teeth of the ring gear. If that plate is damaged, you probably need to buy a new starter motor, or else your newly installed ring gear will have a very short life. After market starter motors with new bendix installed can be had for about $125. If you buy one, check the long bolt length, as I have had them snug up against the backside of the flywheel, making the motor impossible to turn over. The bolt closest to the side of the engine block is the one that can make trouble. I have replaced a few ring gears also. When you replace the ring gear, you need to remove the entire flywheel from the crankshaft. Check out the condition of the clutch and pressure plate at the same time.
Paul in MN