From what I understand the New Republic is considered the successor of the Empire. So I would suppose most of the remaining troops would pledging their allegiance to the Republic, and it would have control of most (former) Imperial installations. From my point of view it would be illogical to completely disband this - sure, punish the war criminals, but the rest would be needed. I am thinking along the lines how post WWII German military was reformed - still wearing "old" equipment with new insignia for a long time.
So my question: do we know whether the New Republic uses stormtroopers, TIE fighters, Star Destroyers, AT-ATs, etc?
I understand that the First Order sees itself as successor of the Empire. Still, it seems it was at best at similar strength as the New Republic. Also, the New Republic was in control of most of the area, so they were in need to defend their borders - especially against the First Order. Why wouldn't they use the former Imperial installations and (the now loyal) personnel?