Low power means nobody is going to notice.

For the most part, transmitting radio in the US is only allowed in a few frequency bands, referred to as the ISM band. These have pretty strict transmit power and duty cycle limits. If you get a ham radio license, then many more bands open up to you.

Title 47, part 15, holds the relevant regulations. Subparts 5, 15, and 23 are probably where you should start.

TBH, if you keep your radiated power low and make a reasonable attempt not to interfere with other users (be aware of bands' uses and where your harmonics and spurs are falling), you'll be completely fine, the worst you'll get is an official notice from the FCC telling you to stop.

I'd also suggest seeking out some ham radio experimenter groups to learn from, even if you don't want a ham license, there's a lot of practical knowledge to be shared.