This will probably be tricky if you’re new to after effects. But i think trim paths could work.
You need to make each slice as a separate shape layer, and use one of the slice layers as an alpha matte on top of a very thick colored line (on a separate layer) then when you animate the trim path effect to fill that slice, the line will only show up where the alpha matte is present.
On top of the alpha matte layer, place another slice layer but one that has the lines in place. With some tweaking i think that would work. Once you have one of the slices working, duplicate it and rotate it to fill out the the rest of the chart.
I’d recommend making a null object to use as a control layer also so you can animate the values easier. On the control layer I’d put an expression slider for each trim path effect. Then pick whip the trim path value to the expression slider. This way you won’t have to hop around many layers to animate.