I'd also suggest Audacity to do the trimming. Mainly, because to get the file to 300kb, you'll also want to trim the song down to 30 seconds or so. Here's how:
Install Audacity, and follow the instructions on their homepage to install the MP3 codec (it's really pretty easy). Once that's up and running, open the file you want, select the region of the song you want to use, and click Edit>Trim. Then (if you didn't start at the beginning of the song), Project>Align Tracks>Align With Zero, to bring it to the front of the file.
Under preferences, the File Formats tab will let you select your mp3 option. I'm not sure what will give you 300kb for 30s, but maybe try 64kbps to start. Save it and see how big the file is, and adjust the bitrate if necessary.