Hi @Mr. Productive, I think we're in different time zones, so please forgive me if I seem to be late responding.
I am struggling to advise you because you want both the biggest and the smallest you can have with extreme efficiency. It's the old marketing conundrum of "Bigger, Faster, Cheaper—pick two!" What you need to do is experiment to obtain the biggest (in this case, more pixels) with efficiency (in this case, smaller size).
Expanding on what I mentioned yesterday. I can take an image that is 8 x 10 inches at 300 dpi (24000 x 30,000 pixels, and let's say that has a storage size of 10 MB. I can manually decrease that size to a thumbnail size (I refer to “manually” as taking a corner and dragging it toward the opposing corner), and even though it is smaller, it will still maintain that 10 MB size. When you go to print that thumbnail, your computer will still be dealing with the storage size of a 10 MB image despite its apparent smaller size.
At this point, I need to point out the difference between what you see on the monitor versus what you print out. You mentioned a 4K monitor. That means it has 4000 pixels across the width. If you open up an image that is (say) 8000 pixels wide, it will display 50% of the pixels it has. If you set that image to be printed at 300 ppi, it will still appear the same way. Pixels on your monitor can only be square, one color, and one level of luminance. Period. Monitors are PPI (Pixels Per Inch) and have no clue about DPI (dots per inch); only printers can handle DPI. Images on digital media can only deal with ppi (pixels per inch).
I mention this because in the early days of the internet, people took their vacation images and sent them to friends. These images might be 3500+ pixels wide, but would "appear" to be much smaller because the software would make the image "fit" in the boundaries of the email as if they were 1000 (or smaller) pixels wide. Yet, they'd still have the storage size of the original 3500-pixel-wide image. Thus, it would take ages for this image to appear in the email — the image had not been properly sized for the task.
What I'm getting at in the above paragraph is getting the most efficient size for the quality you want. I cannot tell you how to do this efficiently, because it’s a balance between the highest quality and how long you want to sit in front of your computer waiting for it to finish any given process with these images.
Oh, let me give you one other stumbling block: compression. You did mention JPG images. JPG images are smaller than their PSD or TIFF companions because they delete every 8th pixel across the image. Actually, they may delete more or less, depending on the amount of compression. Now, that may seem horrible, deleting pixels, and it is. But, often, it doesn’t matter. However, if you have a photo of nothing but leaves and flowers, you’d never be able to see this loss. But if you have a photograph of a telephone pole against a blue sky, you will see a lot of stray pixels floating around the arms of the telephone pole. (You may have also received a flyer in your email that was a JPG image, and the text is fuzzy because the sender over-compressed the image to make it smaller.
But, here’s the deal on compression: if you take an image, make some adjustments, and save it as a JPG. Then the next day, repeat that you are “JPGing a JPG.” In other words, you are increasing the degradation of the image by repeatedly saving the image over and over as a JPG image. You can speed up the degradation process by using a lot of compression the first time around. Using Photoshop’s range of 1 – 10 compression, where 1 is a lot of compression and 10 is (essentially) no compression, a low number is a lot of compression and therefore results in a lot of degradation on the first save. It is generally accepted that “around 7” is a good compromise between a smaller storage size for the image and the least amount of degradation. But this is entirely subjective. What I consider “least,” you may consider complete destruction. (BTW, the way around collective JPGing a JPG is to always save the image in either PSD or TIFF format until you know what the final save is for.)
So, let me sum this up: if you want efficiency, you want a smaller storage size of the image. If you want the best image, you want a lot of pixels. However, below a certain point, you will not observe any significant gains in efficiency; above a certain point, you will not observe any increase in quality.
And for software. Because you are working with images, you need to adjust both their dimensions and the settings of their DPI. Thus, you need Photoshop. The best way to get this into a print format is by taking the images and placing them into InDesign. Here, you can have both the images and any descriptive comments along with page numbers, Table of Contents, Index, or whatever you want. And, when finished, you can press Command/Control-P to print or press Command/Control-E, and you have a PDF where you control the full DPI of any images. I recommend that you get the full Creative Cloud Suite, which will give you far more than you need, and the full Acrobat Pro. Consider this a business expense.
Then, once you have all this software, you will need to experiment with what your objective is and compare it with what you create. Find your happy medium and go for it.
Good luck!
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