I like the 1861 because it seems to be a bit quicker handling than the 51s. I attribute this to the round barrel. On the scale, they both weigh the same but in the hand, the 61 seems more responsive. And when I started shooting C&B revolves the first ones I was given were 1861s. I think I gave $75 for the pair, which was abit high for the times but they were complete and original. Later sold them to a fellow who said I should not be shooting them. Used the $$ to buy a couple of 61s from Uberti. In my hands, they were about the same.
As far as the Pietta, it is a good copy of a custom barreled 1861 but not a Pocket Police revolver.
For a first Colt, I would recommend either the 51 or 61 as the Pocket revolvers are a lot more fun to get to work properly. Learn on the larger frame and go to the smaller one later.
Kevin