Hello hello, sorry if this is too late but DON'T use Audacity to mix music. Audacity is more geared towards making sound effects and raw voice recording. You need a proper DAW to do mixing.
You should download REAPER, it's a free DAW program and I use it almost daily whenever I'm recording stuff. It's a barebones Digital Audio Workbench that has can have the same potential as more expensive DAWs like Logic or ProTools. What you need to understand is frequency carving, or what parts of the audio spectrum that your music is covering over your vocals. This is so that you don't have stuff overlapping each other.
I listened to your recording and I can say that it's NOT your microphone that's the problem, but rather the frequencies that it's occupying. You can honestly get a working tone out of most external microphones as long as you have the patience to work with it. Most of my recordings are done by a Shure SM58 (including my debut EP), which isn't a microphone that modern day recordings use. (It's a dynamic mic, and most mics used in studios for vocals are condenser mics unless there's a certain sound you're going for since it gives the most clean slate to work with)
It has too much presence and high end and in return comes off as "very forward" in the mix while everything else is in the background.
Once you downloaded REAPER if you don't want to get too technical with it, import your backing track and vocals and then go over the FX chain for the vocals. You want to put in ReaComp and just slap on the preset for Modern Vocals, that'll make sure that everything sits properly in terms of volume and doesn't have much variance so that it's more consistent sounding. Next you would want to go to ReaEQ and then basically use the "Stock - 11 band Full Vocals" preset. That'll make it sound instantly much much better than what you have right now.
There's more technical stuff involved with mixing than that, but that's the basic gist of how to mix vocals in.
Hope that helps out!
