So, I started getting a weird beeping noise in my recordings. I don’t know what it is. I don’t know if it’s a setting or something, but I haven’t really explored Audacity very much yet. I would LOVE to remove it. 
That sounds like electronic noise, probably generated inside the computer. It’s quite a common phenomena when using USB audio devices due (we think) to noise being transmitted through the USB power supply. It can also occur with internal sound cards - computers are a hostile environment for high quality audio.
Fortunately in your case the noise level seems to be pretty low, so as long as you are able to record a good healthy signal (peaking at around -6 dB max), then the Noise Removal effect should be able to handle it pretty well - but don’t over-do it. Just aim for a reduction in the noise of say 15 dB and that should make it unobtrusive. Attempting to completely eliminate noise will often damage the audio that you want to retain, so it’s a balancing act between reducing the noise without damaging the retained audio.
http://manual.audacityteam.org/o/man/noise_removal.html
Thank you so much!