static in the background is called "room noise". home recordings will have this because the rooms aren't treated to mute sound as like in a professional studio. this noise is caused by A/C, fans, traffic outside, breathing, etc that is picked up at low frequencies.
to get rid of this start by recording in a smaller space. i assume right now you are just recording in an open room. move to a closet, or another smaller closed off area. the more room there is, the more noise there will be. professional studios spend a good deal of money to get rid of room noise.
you can also use a filter and filter out some of the noise. i've never used audacity, so i'm not sure if it has a filter.
you may also need to stand closer to the mic.
once you have recorded, go back and cut out all of the dead air when you aren't singing. this will get rid of the random static in the middle. it will still be there when you sing, but if you've followed the steps above, it shouldn't be too bad.
getting a better mic, and software would help too