What your trying to do is called a Mashup. so My recommendation is to
get the acapella or the vocal track of the lyrics and just the rhythm
of the music as well as the vocal track. that way you can mash things
up. now doing a live recording for what you want to do is going to be
hard. seasoned DJ's can do it. Get a sequencer software and learn how
to use it. than take samples from the tracks that you would like to
use, than samples of the vocals you would like to use. and you will
trigger the sample for as long as the vocals are going for once they
are done and its time for the chorus. sequence the chorus beat and the
vocals you want to use until you complete your song. this is one way
of re-mixing and its probably going to be the best way to remix music
for you.
So you can e-mail me @ shint...@gmail.com. you can also message me
via Aim using mezicandragon or you can come to Austin TX and i will
teach you in person. if you have any questions please let me know