Need to make this circuit with a different transistor
The circuit is not critical in any way.  Pretty much any small signal NPN transistor would work in that circuit.

Your BC337  should do just fine.  Remember, though, that the pin connections may be different if you are following a wiring diagram.  You will need to check the datasheet for the BC337 and the 2N3904 for the proper pins for the collector, base, and emitter.



The circuit isn't a simple inverter.  A simple inverter would not need the capacitor.

This circuit is used to generate a high signal that pulses low when "STATE" changes.

The capacitor and the resistor form a high pass filter.  This passes only the transitions from STATE to the base of the transistor.

When STATE is stable, no signal passes to the base of the transistor, so no current flows through the collector. -RESET stays high. 

When STATE changes state, there will be a short blip at the base of the transistor.  That voltage blip on the base causes current to flow through the collector and out the emitter.  - STATE is therefore pulled to ground for the duration of the blip.

The duration of the blip depends on the values of the resistor and capacitor.  A larger value for either causes a longer blip.  Smaller values will cause a shorter blip.

Look up "RC time constant" if you'd like to know how that works.