Do I need window trim for a chair rail

This is not meant to be a complete answer, but might help with your understanding of it. My understanding of the physics of windows is as follows -

Nearly all radiation (visible, UV, infrared, every other type too) that travels from outside the house into the house and is absorbed (not reflected back out again) is converted into heat. I would expect that exceptions (such as the energy from UV light causing a chemical change, such as when it fades your couch, or waves that induce a current in a conductor) are relatively negligible.

This means any radiation that can be reflected from the window to prevent it entering the house reduces the heat load. Also, if the radiation is absorbed into the window glass (eg through tinting it), then some of the heat from the window glass will be lost to the outside (through both conductance/convection and some radiated heat) which is an additional benefit.

A heated window pane would like lose more heat to the outside than the inside because the wind would help keep the temperature difference between the glass and the adjacent outside air larger than the temperature difference between the glass and the inside air.

Honestly, letting your wife pick what looks best is the answer. The double tilt sliders are nice if you want to pop them out and clean them I guess. I like the awning ones because you have a bigger window area without sashes in the way. If you do get the awning style, make sure the crank mechanisms are replaceable. I have one in my bathroom that basically isn't repairable without taking the whole thing out. Whether you will actually be opening and closing them and how much airflow you want to have is another consideration. You may not want to have to crank it in an out or remove the screen to unlock it.