Trace aligment in a double sided 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.