Uncovering data from noise
Since my understanding is still fairly low, is DFT and FFT really the solution to my problem?


All the FFT (or DFT) really gives you is a way of visualizing the data in the frequency domain.

Your data may be good for this, except that there will be a large spike at "DC" (the zero frequency bin) because your data has a non-zero mean.


  Would it be logical to take the FFT, filter out outliers that are generated and cause noise, and re-construct the time domain signal back ( with the results that were acceptable ) using iFFT? That should, in theory, give me back a time domain with less noise, no?


If you know the approximate frequency of the variation you're after, yes, you can use the FFT (and IFFT) to filter out frequencies different from the band where the frequency will be.

One simple thing you could try without using an FFT is to use a DC blocker.  That will make your signal approximately zero mean, and will also smooth out some of the roughness you see. 


  Is there a better section of DSP that I should read that can help me analyze the decouple noise from interesting data in a time domain?


One place to start might be chapter 15 of that book.

I suspect you'll want to design a bandpass filter around the frequencies of interest and filter out everything except this band. You will still see some effect of the noise, but it should be greatly reduced.

If that isn't good enough, then you may need to try more advanced techniques which don't appear to be covered by the book.