This is actually a great suggestion, thank you. I've been meaning to try this for a long time, maybe now is finally the time to give it a shot before I waste a bunch of time selling/rebuying.
Is there a site like this that scans manuals? I see they have a section for PS1 games but they don't have "covers," instead they have full manuals so just printing out a picture of the front of the manual would be a little awkward. I suppose I could just print out the backs/spines and call it a day lol. That's all that would really show on a shelf anyways.
I'm late to this, so I don't know what you ended up doing, but yeah, just printing the covers seems like the best idea since, like you said, the spine is what you'll see on the shelf anyway; I think doing the manuals is overkill.
As for the topic, I replaced most of my "Greatest Hits" copies years ago, except a few given they're superior to their black-label counterpart due to having received bug fixes and such. Of those, the first one that comes to mind is Jak X: Combat Racing given the original version has a nasty save glitch that the reprint fixed. Another is Silent Hill 2, which not only fixed some bugs but also included content originally introduced in the Xbox version. However, do keep in mind that not all of these reprints may be the best option since some were downgraded by not having proper fixes, or worse, were censored or had content removed due to licensing issues. And for the sake of keeping the conversation collector-oriented, some of these releases tend to be uncommon, a good example being the "Greatest Hits" version of The Warriors for PS2.
Lastly, worth mentioning are both Metal Gear Solid 2: Substance and Metal Gear Solid 3: Subsistence, which are expanded editions of the original games that happen to be better than both their original and re-released versions.