The original Splinter Cell and Pandora Tomorrow work well enough with some tweaks (
widescreen fixes,
higher resolution textures for the first game). Thanks to
dgVoodoo2 you can even enable the shadow buffer effects that originally only worked on GeForce 3/4 (and maybe FX?) cards. If you have an Xbox One/X/S they're probably better played on there via backward compatibility, though.
As for the remake...I'm trying to be cautiously optimistic. The quality of the games in the series has been very inconsistent over the years. The original is great but noticeably antiquated at this point, Pandora Tomorrow did some neat things in a few levels but was largely a mess and downright broken in some ways, Chaos Theory is great but also hasn't aged that well, Double Agent had some neat ideas that were implemented half baked and had the added weirdness of the differences between the previous gen and next gen versions, conviction is hot garbage and Blacklist was a pretty good soft reboot and a much better attempt at modernizing the gameplay than Conviction was.
That being said, I think Splinter Cell is a good candidate for a remake. I wasn't a huge fan of what they did with Sam as a character after Chaos Theory and I didn't like the way they started simplifying some gameplay elements and the way the games became a little less stealth and a little more action (with conviction being the worst offender). Supposedly, one of the goals of this remake is to keep the tone and more grounded nature of the original while leveraging modern hardware and gameplay concepts...so we'll see how well that works out.
Part of me hopes that they're targeting next-gen hardware, though, because it could be a great showcase for a range of ray traced effects that would probably be difficult if not impossible to fully implement on current gen consoles.