Concerning bike saddles :
Sit on the edge of something hard like a public bench. You will notice there are two bones in your butt carrying your weight. Those are your sit bones and are meant to carry your weight. On a saddle you want these two sit bones to rest on the two bumps at the rear. Girls have sit bones spaced more than guys so you should select a girl saddle.
If the saddle is too narrow, it will press on your crotch, and wedge between your sit bones, and that's not comfortable. You will feel this very quickly. If it is too wide, it will rub inside your thighs and they will get sore. Wear cycling underwear, it works.
If your butt is not used to cycling, all saddles will hurt a little at first after 10-20 minutes. So, at first, do not ride for too long. After getting used to it, a saddle that is well suited to you will not hurt at all, however a saddle that is not suited to you will always be a pain in the ass no matter what you do.
Do not choose a saddle that is too soft or plushy. This may seem like more comfortable at first, but your sit bones will sink too much into the plushy foam, allowing the center part of the saddle to dig into your crotch. This is a beginner mistake : it skips the "getting used to it" part (you have immediate comfort) but after say, 30 minutes it's hell.
Also, adjustment is key, if the front part is too high the saddle nose will hurt you, if it is too low you will slide on it and your arms will get tired quickly.
About the riding position :
In the city I don't like race bikes, position is too low to look at traffic.
Dutch-style bikes appear more comfortable, however being too "upright" is not good. First, you have less leg power. Second, when you ride over a bump, your back and your butt get compressed by the shock. With a slightly "bent forward" position, on bumps your back will just bend a little more, absorbing the bump without harm.
About bike geometry :
Test ride at walking pace, some bikes balance much better than others. This is useful in parks with pedestrians.
Normally you'd need to test ride at a very fast speed too, but I don't know if you'll be able to do that.
About the bike itself :
I won't mention specific brands of bikes etc.
If you intend to really use the bike and get some mileage, get some quality components especially in the transmission, all brands (shimano, sram...) have many product lines from "breaks down completely after 1000km" to "lasts more than 10.000 km if properly maintained". The cheap crap actually costs more if you consider you need to change everything pretty often. In Shimano, get Alivio/Deore range, for example.
Since you're heavy, get a rear wheel hub with a cassette, not a freewheel. Freewheel hubs are cheap junk, break axles, and usually have crap bearings.
NYC is pretty flat but maybe you'll want to cross some bridges or go out of the city for a ride.
You are probably out of shape so your power to weight ratio is going to be pretty bad.
So, if you intend to do any kind of climb, you will need some decent granny gears. This is important, since walking to push the bike will kill your motivation.
If you don't want flats, put some schwalbe marathon plus tires, those are not cheap but last forever.
If you want to go shopping with the bike, you'll need a rack and panniers, and a good lock !!!
Anyway. Last year after a long break I resumed cycling.
I got a fitness/city bike with a decent granny gear (28T front/32T back), good for climbs.
before -> after
weight 110kg -> 100kg and lots of new muscles (still lots of fat to burn though)
tired after climbing 150m -> i'm now at 1500 and 150km in a day
feel much better now too !
If you do the cardio training part right (get a cheap heart rate monitor) cycling is an excellent way to lose weight and (more important) get in shape and feel great...