Or, possibly just 45 degrees clockwise, hard to say which is better (45 deg or 90 deg). Try and see.
I wouldn't make it 4-layer on such a super simple board unless I have unlimited budget. It may be only a few dollars in mid-sized batches, but for small quantity prototypes, the two extra layers would become the biggest expense of the project. Of course, if this doesn't matter, 4-layer will be easier to lay out and perform better EMI wise. It's very hard to see that you'd need to debug power and grounding on such a small and simple board on 2 layers.
Instead, add a few GND stitching vias, they are free. You have enough empty space (read: wide copper pours) and enough pin headers with ground connections (natural ground stitching) there so you could do without, probably, but adding a few would be a good habit. You could try adding a few and then we'll give you feedback about how you did.
1 - components
2 - GND
3 - power
4 - tracking, and more components if need be
And, most of the tracks would naturally go to 1 to minimize vias on signals.