I prefer reading certain books physically instead of by Kindle, and there's one that seems to be in very limited circulation at the moment for physical copies, which has led to the price being $110! It's way too much for me to spend, and since I have the PDF copy, I figured printing a physical copy for myself to read.

Has anyone else done this? Is there a particular program to use to that by the time it's printing all 200 pages (100 sheets, but double sided), the stack remaining in the printer tray will be in order, with page #1 on top? As opposed to page #200 on top and having to rearrange everything?

I pondered having it printed at Staples but there may be some copyright issue they'd tell me 'no' for.

If your printer's output tray is poorly-designed and too small to keep the whole output correctly stacked, you could try printing in small batches (such as 20 pages per batch). It's not like you're pressed for time.

Ah, right. Double-sided. That's a bit trickier. If your printer doesn't have a duplex (most home printers don't), you'd have to print the odd 100 pages, then flip them, re-feed them to the printer and print the even pages on their backs. Unless you've done it before, the process is somewhat unintuitive. I suggest doing a test-run on a small document (4 pages on 2 sheets) to figure it out (Which way the sheets in the input paper tray are laying - face-up or face-down? Which side is up? If you re-feed the output into the paper tray without flipping it, will the double-sided output turn out to be correct?).

Printers generally output pages face-down, meaning that #1 will be at the bottom of the stack, face-down. All you'd have to do is flip the whole stack once you're done. If you do the manual duplex as described above, then you might need to start with the even pages instead of the odd ones to ensure that page #1 is face-down at the end (meaning that page #2 is face-up; if it's the other way around, you will have to flip the whole stack page-by-page indeed).