I think I have an understanding about what your issue is here. You are most likely using beats that are bounced through a limiter and WAY to loud at your tracking/mixing stage. This means you cant hear vocals over the beat in your headphones while recording. While rapping over already brickwalled mp3s is not ideal when it comes to sound quality, I understand that sometimes that all you have to work with.
So, stand infront of your mic, and perform your part as you will while you record. Set you mic-pre level so that you maybe touch YELLOW on your metering once or twice in a verse, if you have explosive parts.Then, in your DAW - Cubase, Pro Tools, Sonar, whatever you use, turn the track that you have the beat on down until you find a good balance between your vocal in headphones and the beat.
Then if you absolutely need to have the whole track LOUD, turn the WHOLE thing up together (beat and track). While this is not ideal, when presented with this particular situation that is how I achieve the best possible results.
You absolutely do not want to record through a hardware compressor, unless you really know what you're doing, or you are using a fairly mild setting on a high-end compressor. "Pros" do it this way, but often times not for compression, but for the sonic character a specific compressor can add to a sound. It would suck to have a great take get ruined by a compressor.