I want to run certain levels, but I don't know the best routes. What should I do? Any tips?

Mania stages are larger than all Classic Sonic games, so they're a bit hard to memorize.

There's the Individual Level leaderboard here. What worked for me when trying to learn the full game was training each level trying to replicate what the players with best times do (aside Oil Ocean 1, where I tried to create my own route when the game was launched). It's a bit hard at the start, but training makes you get better at it (like almost everything in speedrunning).

Here is what I did:

Looked at the sticky maps in the forum.
Watched the Individual Level Leaderboard runs.

Then you'll have to practice too. Time Attack mode or debug mode.

dev menu is also helpful for learning boss strats/strats where you take a shield from act 1 to act 2