The original Paper Mario remains my favorite of the series... though it's a close call. I played this game as a kid on Wii Virtual Console after Super Paper Mario (though I was probably stuck between Chapters 3 and 4 at the time), and it was likely my introduction to turn-based RPGs (either this or Super Mario RPG). There's a certain unique charm to this game... I think a lot of it comes from the graphics and the humor. As for the graphics, while the whole “2D sprites in a 3D world” is the big thing of every Paper Mario, I dunno, it just... feels different here. Characters are a lot more expressive, and don't feel arbitrarily locked to the four perspectives of left, right, up left, and up right like its sequels would. You'll occasionally see some sprites at other angles, which is nice, even if it feels like such a small thing to go on about. The game also has a lot of attention to detail in its sprites compared to the other games. Like, there's distinct animations for eating or drinking items, and they also went through the trouble of making three different battle entrance animations for Mario and five battle exit animations! Not to mention Mario's little ready stance before he jumps, and the three different jump attack variations he has for the game's three different sets of boots. It all exudes a certain kind of charm in that regard.
The humor's a lot subtler than the later games, I feel. As the series went on, the jokes would become more overt with each game (and that's not a bad thing! I think Color Splash and Origami King are some of the funniest games I've played), whereas here the jokes play into this sort of whimsical feel hanging over the whole game, and honestly... it's not always easy to tell if something's meant to be a joke, or just something I found funny. Either way though, I'm smiling at the text all the time. It's one of those games I never picked up on as being particularly funny as a kid, but now I'm able to tune into the subtler comedy and appreciate it a lot more.
As for one more thing to gush about: the letters. It's such a small thing, but throughout the game, not only will Mario receive letters at his house from people you've met along the way (complete with charming little photos of them that nail an art style the series would never bother with again (same for the little portraits that show up whenever a new partner joins you)), but your partners will receive letters from people close to them that they've left behind to join your adventure at a dedicated post office. Again, it's a tiny little detail, but it works so well to help the world feel alive. Overall, that feeling of liveliness is something Paper Mario excels at.
Of course, the foundations set here are great too. While the combat system isn't as refined as TTYD's (there's a certain very abusable tactic I found that took some of the fun out of it) and the characters don't get quite as much depth as TTYD either, they're still strong aspects of the game. The improvements of a sequel don't necessarily detract from what made the original great. While there's a strong formula for each chapter (exploration, new partner, dungeon, boss), the locations you visit and kind of characters you meet in each place are varied enough to keep it interesting (gotta love Flower Fields for bearing practically no connection to anything in main series Mario... it's a little hard to look at and then go play any of the modern Paper Marios). The story's a simple “Bowser kidnaps Peach!” approach, but there's so much more life to it than certain future games, and the little Peach interludes between chapters break the pace nicely while making it clear that Peach isn't just sitting around. The story's stakes might not be given as much weight as the next two games would, but Bowser's goofiness suits the whimsical tone of the game well. TTYD might be more grandiose in every aspect, but the original Paper Mario set the foundation that TTYD would build off of, while retaining such a charming level of detail over its successor that I just can't ignore.