Designing a PCB with multiple supply voltages
Should I just place a big ground plane on the bottom and connect
  everything? Or perhaps a star topology?


Big ground planes are best in most designs. They reduce inductance and resistance of return currents because there is more copper for the current to flow on. They also increase the amount of capacitance to other traces/planes which is good to knock down high frequencies by shunting high frequencies to ground. 

A point where you would not want to use a solid ground plane is if you have large currents that could run on the ground plane through a sensitive area (like low level analog or if the voltage needs to be maintained to less than 100uV) because the resistance of the plane can create a voltage offset. In this case you could either move the components away from the return current on the ground plane, create a slot or split plane. Slots and split planes come with their own problems (can become radiators) so use them with caution. 

If the design is purely digital, a solid ground plane would be recommended.