Check if your university is capable of making its own boards. If so, you'll have to etch it yourself so try to make it single layer, and use jumper wires where necessary. In that case, use through hole components and route the traces on the bottom layer. If they're capable of making double sided boards (same process but need double sided copper clad board and requires a few tricks to align the layers) then you can route on both layers. However, keep in mind that not all through hole components can be soldered to both sides (headers for example which can only be soldered at the bottom side). If you have a rivet press you can use vias.
However, for a university project I assume your board won't have a high part count, and thus the board area will be rather small. If you've never etched a board before and aren't planning to do it often then it's probably more cost and time efficient to send the design to a Chinese PCB fab (I prefer Iteadstudio) which manufacture professional boards (double sided, solder mask, silkscreen overlay) starting at $20 including shipping worldwide.