Marill to me feels like a Gen. II Pikachu, so I'd imagine it being one of the most popular (at least aesthetically). There's also Pichu (which I personally favor over Pikachu, barring its modern Sugimori artwork).
Strictly from a design perspective, I think Sneasel would be my own favorite with these limitations. The original card was nice, but Dark-Type moves being Special in the GSC days made it pretty much unusable in the video games. Misdreavus, another Gen. II favorite of mine, suffered a similar fate with Ghost-Type moves being Physical.
If you define popular as Pok?mon that you're more-likely to encounter on another player's team, I agree that Ampharos and Togetic would likely be some of the more common ones. Maybe Quagsire as well.