Observations:
You are basically correct in all respects and a base current limiting resistor is essential or it will burn out.
Note that a reed switch will probably 'bounce' it's contacts so you may get irregular timing and they also have limited speed and lifetimes. You may be operating it tens of times per second so it probably wont last long. A 'Hall sensor' would be a better switch as it has no moving parts.
The other issue is the flyback spike. The diode is essential to protect the transistor from high voltage but remember it's high voltage you actually want. A higher voltage rated transistor might do the job, maybe a BU2506 or similar and omitting the diode or replacing it with a snubber network.
Consider what happens when the switch opens, ideally the base voltage will drop to zero immediately but in real life, leaving the base disconnected will leave some voltage on it from internal leakage and stored charge. You would have to add a resistor between the base and emitter (ground) to leak the charge away. To do it quickly the resistor needs to be fairly low in value, maybe 470 Ohms or less.
Brian.