How to record your singing with a song?

Okay, I tried to record someone singing and then mix it with a song,
but the beat would always get behind or too fast because you have to
take the time to click play and stuff.
I found a neat program called AVS audio editor but the beat is also
late, and when i saved it to my file,
it would keep saying "demo" between every few seconds.

I want a mixer that can mix a person singing while the music is
playing...

and i don't want the free version that doesn't even let you save your
recordings.....

Anyone know a really good audio mixer that you can sing with the song?

thank you !
that would be really helpful