First, what are your source clip settings: frame rate, pixel dimensions and compressor (also known as codec).
What are your sequence settings: frame rate, pixel dimensions and compressor (also known as codec).
Generally, source frame rates should match sequence frame rate with one exception. FCP can deal with 23.976 fps material in a 29.97 fps sequence, but the conversion is not ideal.
Here's a user tip spelling out the issues.
Also, source and sequences should always be in a fcp friendly format. h264 is not an fcp friendly format.
Compressor will do a great job of converting most formats and frame rates. Here's some tips regarding compressor