Electronic – High Voltage PCB

It depends on the speed of your signals. Signals with really fast edges or high frequencies have different requirements. You'll need to treat them as transmission lines and control the impedance and length and everything. For slower signals, a good rule of thumb is to try to route one layer horizontally and the other vertically to reduce noise coupling like you mentioned in planes. You can also try to route all of your signals on the top layer and flood fill the bottom layer with ground copper. That will help decouple your signals and give you some extra parallel capacitance (which is a good thing). Don't be afraid to use multiple vias on the same trace if you expect higher current there. Try to avoid vias under ICs unless they're tented because you can accidentally short an IC pin to an exposed via when soldering and you won't be able to tell.

For 2OZ copper, 1cm of 20mil track is about 5mOhm. Assuming your mcu sinks a max current of 100ma, you'll get a vdrop of about 500uV. This is pretty tiny. The inductance will likely not be a big deal either. With microcontrollers, the most important thing is how quick the current draw changes. You can mitigate this by putting a small decoupling cap as close to the IC supply pins as possible. This is what inductance affects, so you want to make the loop as small as possible (i.e. the length is more important than the width).