NT 3.1,3.5,3.51, 3.51+Shell pack*, NT4, are ALL 100% 32-bit applications. they can run 16-bit applications via the use of the virtual 8086 features of all processors since the 80386.
Using ANY version of NT for old games will NOT work. DOS games run no better- in fact, probably much worse - under older versions of NT then they do under XP/Vista. Why? Well, it wasn't a consumer OS until XP... business don't care if DOS games work- they might have some old apps running via DOS but for the most part these are "businessy" text applications that work find under the NT VM.
Driver wise, an NT4 driver *might* work with 3.51, since a lot of NT4 drivers were really just NT 3.51 drivers made "shell aware". Additionally, for the most part NT4 drivers were tested using the beta of NT4 which was the (soon to be explained) "shell option pack" for NT 3.51.
For the most part, it depends on the device. In fact, you'll be lucky to find a driver at all. Best results will obviously come from using a driver designed for the right version. Just remember that windows 3.1 drivers will not work- and neither will Windows 95 drivers.
explorer shell introduced with windows 95. It fell behind schedule though, so aside from a few beta's it wasn't actually released. It did, however- change NT 3.51 into NT4 version-wise (in an attempt to prevent applications from getting confused over versions and having to determine if they can actually use the features present in the shell pack). In reality, NT3.51 and NT4 are no more different then NT 3.1 and NT 3.5, kernel wise- of course there were a few changes, which are inevitable, but for the most part it wasn't a huge departure in any department other then the GUI.
