As a fellow New Yorker and someone who owns five different pairs of Bean boots, I have some thoughts that might help you.
I assume we are talking about versions of the traditional Bean hunting boot (the classic, as Bean does sell modern boots as well)?
First, the one negative, there is no way around this, the bottom of the boot is fine, even good, on NYC pavement and sidewalks in rain and snow, but it is - and this is the only word for it - terrible on the various metal surfaces on NYC streets and sidewalks (manhole covers, grates, those huge metal construction plates they put down over incomplete road work, etc.). For me, I enjoy the classic boot so much and find it has enough good features, that I just accept this negative (and am careful, very careful, as the Bean boots slide on metal surfaces like they are glass).
As to your questions, your instinct is correct in that the six inch height is fine for NYC rain and most snow, except for the one, two or three times a year we get a real snow storm. And, yes, a Merrell (which I used to own) can serve the same purpose (but without the fun or "style" of the Bean boot).
Additionally, your instincts are also correct in that - to truly cover every situation - you need at least two boots. I've acquired mine overtime, but the two I use the most are the six inch unlined one for, as noted above, all but the big snow storm. For those storms, I have the 10" Shearling-lined boot - both the height and lining are great in those situations. I'd buy the unlined 6" first and, then, the 10" Shearling - once you have those, you've pretty much got it all covered.
As to sizing, once again, your instincts are, IMHO, spot on. I'm a 11.5D in a shoe and I have the 11M Bean for my unlined ones as I want those to fit more "normal-shoe" like so that I can wear them with a mid-weight sock (especially in the summer) and walk a lot in them comfortably. Then, I have the lined 10" ones in 12M so that I can wear a very thick sock with them and still have the "air pocket" Bean mentioned as I only wear these on very cold days and in snow.
Hope this helps. Please let me know if you have any other questions.