Mr. Mime and the other region exclusives are all obtainable through eggs as well; as for it being the most rare, that's pretty hard to exactly say as that depends on your location. Some people might live near a Mr. Mime nest where they spawn commonly where as others can go 20+ levels and not even see it's silhouette in the nearby tab. Example, Eevee and Growlithe are common where I live, I would say they are about as common as Weedle/Caterpie are to rural players, yet a few of my friends have seen barely a few of either in all their levels, the Pokemon that are common to me, are rare for others. So even rare Pokemon such as Mr. Mime can actually be a common Pokemon for some.

Either way, congrats on the catch, what CP is it and have you checked it's IVs yet?

Nice find man! I caught one in the wild the other day but it's only 414CP which is a bit crap for a level 25 trainer