YAAAAAAAAAAAAAAAAAAAAAAAAAAAY! Definitely joining this club ;)
Two cute Pokemon: Pidgey and Teddiursa
Partner Pokemon: Pidgey
As for which Pokemon I find the cutest, definitely Eevee, which I'm sure most people would agree on. I love Pidgey to death, and I think it's a pretty cute Pokemon, but it doesn't really live up to the cute standards of some Pokemon, where I think Eevee is at the top. It has a disproportionally large head compared to its body, and pretty big eyes, which I guess are two of the most common cute features, and even though those features aren't exclusive to Eevee, I just feel like its design is the most "aww-inducing" :p Pokemon that, in my opinion, come close to Eevee, would be Teddiursa and Growlithe. Those are just some of the first Pokemon that come to mind when I think cute Pokemon, and both have generally cute features.
So yeah, just my opinion on some of the cutest ones, but it's definitely subject to change, since I just mentioned those that first came to mind :)