What are the advantages/disadvantages of a transmission vs a reflection grating? It seems like a transmission grating would be easiest to use. I'm trying to get a spectrum from Thomson scattered light in a plasma. The broader the spectrum of the scattered light, the hotter the plasma. It's a weak effect, so it's important to keep as much light as possible. It would also be important that the image of light is not distorted (at least not along a chosen axis... obviously one direction will have the light spread).
Transmission gratings are less effective if they consist of absorptive grooves. Thus, transmission gratings make sense to around $1000$ lines/mm. There are also holographical transmission gratings, where the spatial variation is not seen in amplitude but in phase. Those gratings show - of course - a different behavior in its spectrum, but have higher light throughput/efficiency.
Reflective gratings, on the other hand, reflect all light and modulate only the "not-wanted" light. Thus they have better efficiency and - as said already - maintain the polarization in a better way.