How to build a Real Nuclear Reactor?

The best way to build one is, VERY CAREFULLY.

Get an education, get some money then get permission from whoever you need to, then make it!

Even if power lines went down, it wouldn't be for long.  When this happened decades ago, it wasn't a tragedy.

If you are concerned about continuity of power, I would suggest the same solution that hospitals and computer centers use - have a backup generator, fueled by diesel.  That would cost far less than the mere fuel for a nuclear reactor.

In the former Soviet Union, they had small reactors for single apartment buildings, but I don't recall anything sized for individual residences.  This would be considered a hazard in most parts of the US today.  Besides the direct radiation, there would be the concern for security, in case something happened, like vandalism, or a gas main blowing up nearby.  Making a bomb would not be a concern, if the reactor was powered by Thorium, or another element unsuitable for bomb-making.