Make sure the hot side is adequately cooled. Water cooled if possible.
Insulate the cold side as well as possible. You have to cool not only the heat generated by the TEC and the load, but also conduction, convection, and radiation heating the cold stage.
Watch out for condensation. The heat of vaporization is *huge*, so condensing water releases an enormous amount of heat. Also, if liquid water gets near the TEC element itself it will conduct heat between the hot and cold stages very well.
For a 2-stage solution, you need to make sure that the wires going to the upper stage are thin. Fat copper wires will form a thermal short-circuit and reduce the effect of the first stage. You want to balance resistive heating vs. heat conduction. Likewise, make sure the wires powering the load are as thin as practical, and thermally anchored to the intermediate cold stage. You probably want to use something like thin magnet wire with a thin varnish coating to heat sink, it is really hard to cool wires through thick insulation.
Don't use PWM or on-off control. Filtered PWM is fine.
Feedback loops are hard to get right. Especially if you are trying to get the coldest possible temperature. The problem is that "cold side temeprature vs current" is stupidly non-linear, and of course if you exceed the current for coldest temperature, it starts heating again as I^2R heating overwhelms the ability of the TEC to move heat. This makes it hard to get a feedback loop that is stable in all these conditions, and can easiliy be pushed into positive feedback and overload your TEC. Start off with manual constant-current control.