Well if you keep to a 2 layer board you can't have 2 power layers because then you are left with no signal layers... The obvious solution would be a 4 layer board but i guess here it would be overkill.
What i would do and have often done in fact, in a case like this is to use a 2 layer board with bottom layer dedicated to ground plane as far as possible. The last bit means that i do route some signals there as well, but always keeping the return current paths in mind, so as not to interrupt the plane with a transverse trace across a return path. Not the easiest thing to do in all cases, but usually with time and patience you will get there. Then the top layer is mostly reserved for positivce supply routing and signaling. All unused area on top is flooded with copper connected to supply voltage, thus creating low loss bypass capacitance against the ground plane. Works like a charm, at least if you keep below say 50 MHz, maybe somewhat higher, and give priority to HF signal routing.
This method won't really work anymore if you get to frequencies where signals need to be terminated and length matched. Then you are in transmission line land, and quite different rules apply. Making a transmission line with proper impedance levels in 2 layer is cumbersome and 4, 6 etc layers are indicated for purely electrical reasons. But not at 40 MHz yet, so my recommendation above stands.