Do Peltier and heater make a good combo for thermostat?
The Peltier can be used as a heater as well, just invert the power connection. But this kind of precision is very hard to obtain, no matter how you heat or cool down. The reason is the thermal inertia of your system: switching on the Peltier if the temperature rises won't result in an immediate temperature decrease. So you'll have to model the thermal environment and use a PID regulator which takes the thermal inertia into account. To get 0.05°C precision the environment has to be extremely stable, which means very good isolation from the outer world.
It's not impossible, but anything but easy.  

Temperature stability is a requirement for meaningful 24-bit ADC, but you'll also have to take care of offsets and (thermal) noise. Offset case in point: ADCs usually have low impedance input. A 5 cm trace to the input may give an error of several bits! 1 LSB in 5V is 300nV.