Re: pcb track below the components
It al depends of the circuit needs. If it has precision analog parts, then a single sided will allow too much ambient noise to perturbate the signals. If it's a high speed circuit, then crossing paths is not a good idea due to EMF generated by tracks (that theorically doesn't affect if they are perpendicular, but that will make the routing labour much longer and delicate, whithout saying it might take more space, increasing manufacturing costs which I see it does matter in your case).
There is absolutely no problem in pure digital signals and supply tracks to be crossed in any part, but keep in mind the implementation of 100nF decoupling capacitors near the ICs. The same doesn't happen with an ADC, which is digital but needs (or it should have) a very well filtered and noiseless supply to get accurate measurements.
Auto routing? I personally don't like them, but you always have the choice. If you can afford a 2000USD licence to a good auto router, then you will have to spend about an hour or more to configure it (tracks widths for each class, clearances, positions, rotations allowed, rooms, connectors zones, etc) and then wait till it gets it done. Sometimes you will not get the spected results.
I prefer to trust the human capability to place each thing in its place, ordering the sub circuits and keeping space for silkscreen notes. Oh, and making it easy to repair if it would suffer any failure.
As you mention a USB, I assume (it could not be too) it's purely digital, so a single sided PCB should work fine. The SMD micro USB is smaller and has more soldering area. The male (class A) connector needs holes in the PCB (thing you don't seem to want) but it seems stronger, since the through hole terminals give an extra mechanical resistance, and a disadvantage of it is that if connected directly to the PC, it could suffer a strain that could damage both PCB and PC port.