So when you get to the first ring, should I be throwing an eye of ender every 100 blocks or so? What is the ideal distance to travel before throwing another eye? And obviously i know to throw an eye before traveling into the ocean, or before a mountainous biome, etc.

well basically you wanna blind travel then estimate the distance and then throw when you reached ur estimation

Use a triangulation cheat sheet (like this one: https://imgur.com/gallery/PUsG4Cc) to roughly calculate the stronghold distance. With this strategy, you shouldn't need to throw more than 3-4 eyes.

@Alivingcreatur so for step #2, would I just be moving 20 blocks away at 90 degrees from the angle of the eye? Also instead of memorizing the table, is there an equation I can use?

couriway's trick is throw the eye. run 20 blocks (4 sprint jumps) and throw another eye but 90 degrees off your first angle. Then 1000/angle change is about the distance to the stronghold. On that base you can decide when to throw your eyes.