What you are suggesting is a little dangerous and might not be that simple.
Simplest, most expensive, but guaranteed to work approach, get a Uninterruptable Power Supply (UPS), DPDT relay and current sensor. The DPDT relay is wired so that either the mains or the generator can run the UPS. The UPS output runs the room. The current sensor monitors the room current and at a preset trip point switches the relay back and forth. The UPS will prevents a power glitch in the room circuit at switchover.
Still simple, less expensive, not guaranteed to work approach, DPDT relay connect between the mains and generator and drives the room circuit directly. The current sensor still controls the relay. Downsides, power will blink off as it switches back and forth. The holdup time of the PC power supply might be good enough so the PC doesn't restart but since the phase of the generator and mains is not matched any inductive motors will cause a current surge and possibly cause the current sensor to falsely trigger.
The very complicated way, Rig generator to run phase synchronous and match level with the line and then when the switchover happens it's seamless. Not sure how that would be done in your case but that's how it's done at power plants.
No matter what approach is used there is a element of danger. Mains switch over units are designed with a lot of safety provisions. I have never designed one so I can't advise you on those safety features. But if you do something make sure you fuse / circuit break all connections into the switch (relay) and make sure the mains can never get connected to the generator. There could be other issues that I'm not aware of so take this advice with a grain of salt.
Ray