There's a Subway Shop with enthusiast books etc inside Grand Central station. It's a bit hidden away but signs will get you there. The Subway Museum is in Brooklyn in an abandoned station and well worth going to, they have one each of a whole range of different cars over time. Because it's still connected to the system they get them out occasionally for railtours.
For express/local, get one of the subway maps which describes the quite complex arrangements. On the four track sections through Midtown Manhattan the express are in the centre. Contrary to what I often see written elsewhere, the bulk of the subway is not four track, but tourists in Manhattan tend not to get too far out. On the elevated sections, which are worth seeking out, a number are three track, the fast track in the middle is used in the am peak towards Downtown and in the pm peak away from there. If you get the chance, ride out to Coney Island on the D train, which is elevated, and at the end passes through the huge depot and workshops which makes the London Underground one at Neasden look like a sub-shed. To the east of Coney Island station there are even double-deck elevated lines, on a huge structure.
Signage is somewhat inconsistent, and when they change their style they seem to leave half the old signs up anyway. Real New Yorkers still know the Subway as three divisions, the IRT (numbered lines, with smaller cars), IND (lettered lines, first half of the alphabet) and BMT (second half of the alphabet), and there are still many signs to this effect.
There are no countdown signs on platforms, but if you can take either local or express, look down the tunnel to see what's approaching. A number of the lines run at surprisingly wide frequencies outside the peaks if you are used to London, say every 10 minutes, or even less, although again unlike London the huge 10-car trains never seem to leave anyone behind, once they turn up.