is spec'd at less than .5C at your temperature range. A small motor driver
will allow you to reverse and control the current through the peltier; ideally the motor controller should be capable of the full amperage requirement of the peltier but in your case, at almost room temperatures, you more than likely won't need to be driving it with that much power. You'd need to calculate how quickly the film bath cools off to understand how much power you'll need.
The PID library
will help you with controlling the peltier based on readings from your temperature probe. The code and examples are a little hard to grasp (it seems to operate almost magically) but I'll guarantee it will be the simplest and best way to do it in the long run.
A DC pump can be pretty easily controlled with a mosfet
; an AC pump should use a relay.