What Order?
Here is the short story: Lightroom -> DeNoise -> GigaPixel -> Lightroom -> Sharpen in that order. Of course, you may not need all of them in every situation. I should also mention a return to Lightroom occurs between each step in this tutorial. I did put Lightroom in before Sharpen, and I will explain that later.
DeNoise
The obvious use for DeNoise is when you have a photo with noise either due to high ISO or low light or a combination of both. Another time to use DeNoise is when you are going to get noise because you are going to use a tight crop. A tight crop will show noise that you never saw before the crop. Use DeNoise BEFORE you crop or do too many adjustments in Lightroom. In Lightroom do adjustments with white balance, lens corrections, or camera profiles on the raw file before DeNoise. It has been found that DeNoise works better on "flat" photos, so do not adjust the contrast or any of the sliders for texture, clarity or dehaze. I also lower the sharpening to 0, but this is not a generally agreed upon setting with other photographers who use DeNoise. DeNoise can do some sharpening as part of the process and if you use it in full AI automatic mode, it may apply some. That is why I put the slider to 0 in Lightroom. I also sharpen at the end of my overall workflow either in Lightroom or Sharpen.
When you chose DeNoise from the Edit In command select Edit a Copy with Lightroom Adjustments, use a 16bit TIFF as this will keep a high resolution. It will also be a large file so you can use compression on it without degrading your image quality, TIFF compression is lossless. The resolution depends on what you are going to use the final image for, digital only, print, etc. The plugin is set up by default with 240 DPI. Either way I keep my own at 300 DPI, but you can go higher or lower. Epson apparently recommends 330 for printing on their printers. Again, it depends on your need.
GigaPixel
It may not be clear what GigaPixel does. GigaPixel increases the resolution of an image. Why would you want to do this? A heavy crop will leave you with a small number of pixels left in an image you may want to print in a large size. You may want to print any image in a large size and want to make sure you maintain quality. Using this after DeNoise, if you need to use it, will increase the resolution without increasing the noise level.
If you did not use DeNoise and make the recommended adjustments to your raw file, do them before using GigaPixel. I use the same settings for Edit In: 16 Bit TIFF, 300 DPI, and compression. In GigaPixel choose your options for how much you want to increase the size, then return to Lightroom.
Sharpen
I do not always use Sharpen just to sharpen my images. I do use Sharpen if I have missed focus, have motion blur from the subject or camera shake from me and I will not make Lightroom adjustments before using it (except the same ones recommended before DeNoise and GigaPixel if you did not use those and are starting with your raw file). Back to the top where I had Lightroom before Sharpen the use case for that would be if I was to use Sharpen just to run a final sharpening on the image. If I am using Sharpen for correction that Lightroom step would not be in the workflow order. Otherwise I just sharpen in Lightroom. I find the AI for these issues works well in some cases, and in others not so much. It cannot correct the "uncorrectable" but it does try and I have found it can make an image useable that was otherwise not. Once again, I use the same settings when leaving Lightroom. In Sharpen I usually start with the AI automatic mode but if I am going to make more adjustments in Lightroom I turn down the sharpening amount and do it in Lightroom later.
I do not often make any adjustments between the three if I am using more than one of them. Once I finished with the last one I am using, I make my adjustments in Lightroom as I normally would adjusting contract, colour, texture, etc. After I am finished, because I tend to use the Edit a Copy with Lightroom Adjustments, I go and delete the intermediate images that got created. I like to keep these while working so that I can go back to a last known good image.
