There are natural accents in the time signatures. With accents on a scale of 1 (strongest) to 4 (weakest):
2/4 goes 1 - 3 | 1 -3 | ...
3/4 walzes go 1 - 3 - 3 | 1 - 3 -3 | ...
3/4 mazurkas go 3 - 1 - 1 | 3 - 1 - 1 | ...
4/4 goes 1 - 3 - 2 - 3 | 1 - 3 - 2 - 3 | ...
It is important, especially with Chopin's music, to know the differences among waltzes, mazurkas, and polonaises. They all accent different beats, even though they are all in 3/4 time, and thus have different feels to them.
Also, upward runs tend to crescendo and accelerate, while downward runs tend to decrescendo and deccelarate.
"When is it OK to vary your tempo and how do you know when you are doing this so much that it is no longer dramatic but is just annoying? How about figuring out the right speed for a piece?"
Actually, I will answer these questions with other quotes:
"There are many ways of performing a given work, but the artist must be convinced that his way is right. That is what gives authority to his performance." -- Byron Janis
"An artistic interpretation may be close to or far from the composer's indications. But one thing is absolutely crucial: an interpretation has to be convincing." -- Shostakovich
"Today’s audiences go to the concert hall to hear Beethoven and Schubert and Brahms and so on. But back in Godowsky and Hofmann’s day, we went to her what the pianists had to say about the composer; we went to hear the pianists, and the same thing went for every other great pianist. When you went to hear Cortot play an all-Chopin recital, you went to hear what Cortot had to say about Chopin." -- Jorge Bolet
"I must tell you I take terrible risks. Because my playing is very clear, when I make a mistake you hear it. If you want me to play only the notes without any specific dynamics, I will never make one mistake. Never be afraid to dare." -- Vladimir Horowitz