Battery Charging Ciruit

Battery circuit design to allow product to become portable.

We have a portable system that is typically plugged in to the wall. It
has a peak current draw of 650mA with all components and display. We
are using a wall adaptor that provides a 12Vdc output with 1.5A rating.
We have sourced a battery that can handle the load. The following are
the battery specs:

Battery spec: 12V 3350mah
configuration:3S1P 18650
cell capacity: 3350maH
discharging current: 1A 

We need to have a circuit designed that we can dissolve into a
custom PCB. This circuit must be able to run the monitor from wall
power and switch to battery instantly when unplugged from the wall.
We would like the battery to get charged while the monitor is plugged
in, whether the monitor is turned on or not. Ideally, we would like to
have a way to measure the charge so we are able to potentially
display the percentage charged on our monitor if it is on and running.
The ability for the monitor to know if the unit is running off of the
battery or the wall power. We would like to have an indicator light that
can show when the battery is being charged or finished. * maybe a
blink when charging or solid when charged. We have the ability to
add a light into our design.