Hi Geoff, you've done a great job with some first images there - well done!
Entering into the world of astrophotography can be quite daunting, there is a lot to learn and often it can seem a bit overwhelming (it was for me at least). However, if there's anything I'll say is that there's an amazing online community with ample guides available and many people willing to help out. Keep chipping away at it and you'll find it incredibly rewarding with the progress you make.
As the others have suggested, flat frames with assist with removing vignetting from your images. I suggest having a good read about the different types of calibration frames that are often employed to improve images and reduce errors that are inherent in cameras etc. The common ones to read about are Flat frames, Dark frames and Bias frames - this page should give you an overview of what they are and what they do
http://www.rawastrodata.com/pages/typesofimages.html
Stacking will certainly help, the idea being that we want to increase the signal-to-noise ratio (SNR) of our final image. The precious signal from that target we are shooting is essentially always there, whereas the noise from the camera is random, as such if we take lots of images and stack them the noise is averaged out.
That is a very basic overview and I suggest reading further into it - there's a ton of really great resources out there that will explain it better then I ever will. Overall though, great first effort - I'm sure you'll become addicted like many of us in no time!