Where can I find a cheap way to mix music?

I have a group project in my world history class to create either a song or skit about the events that occurred during the French Revolution. My partners were going towards the idea of doing a skit because they did not want to go through the trouble of making a song, but I volunteered to try and write lyrics to a sort of compilation of Black Eyed Peas songs, since it would both be fun, easy, and worthy of an easy A. I already have lyrics down to two different BEP songs. One is the introduction, first verse, and chorus of "Let's Get It Started" and it talks about Louis XVI. I have finished a little bit of part of "I Gotta Feeling" to play as a sort of introduction to the song (I gotta feeling that we should start a revolution). Writing the lyrics won't be a problem for me. The problem, however, will be mixing together the music to make it sound good. Obviously, cutting off the thirty seconds from each song that we are using will be a must, but a good way to transition between each song will be difficult for me. Is there an easy way to transition them? I think I will be able to find instrumentals of each song somewhere online or just go get a karaoke CD. Another issue will be trying to get good quality with a webcam. If anybody knows of any good, cheap ways to get all of this done, please let me know! Don't berate my project either!