I am a learning newbie. I am trying to find online a circuit that is safe and effective for creating a battery back up for my modem which is 12 volts, 1.5 amps, my router which is 12 volt and 3 amps, and a WYZE camera, which is 5 volts, 1 amp. I would also like to add a charging port for a phone.
i have a 12 volt, 19 ah sealed battery for the project. I would like everything to run off mains power and the battery to float charge (but not overcharge) when power is available but switch to battery automatically when there is a power failure. I will have to figure out some sort of housing to put everything in to put beside tv in living room. Can anyone help me find a plan?

 

OK, an easy set of devices to power until you get to the camera and phone charging parts. IF you have an adjustable and regulated 12 volt mains powered DC supply then it can "just" be a matter of setting the power supply voltage to the battery recommended float charge voltage and connecting it to the battery. Other schemes will be a bit more complex, if that sort of supply is not what you have.

 

As MB2 suggested you could use a mains-powered 12V adjustable, ≥8A supply set to the battery float voltage (typically about 13.5-13.8V) which should be okay to power the router and modem directly, with a 12V to 5V buck converter to power the camera.
The charging port could be a car-type USB adapter that converts the battery voltage to 5V.

 

As MB2 suggested you could use a mains-powered 12V adjustable, ≥8A supply set to the battery float voltage (typically about 13.5-13.8V) which should be okay to power the router and modem directly, with a 12V to 5V buck converter to power the camera.
The charging port could be a car-type USB adapter that converts the battery voltage to 5V.

But won’t that reduce battery life by constantly pulling off the battery instead of the battery just be in the back up

 

But won’t that reduce battery life by constantly pulling off the battery instead of the battery just be in the back up

No.
The 13.5V supply is providing the modules current along with also keeping the battery trickle charged.