Location is key. It should provide the best views of your garden and also belong to its surroundings.
A Wood burning stove. Not only does it make the place warm and cosy, it will also dramatically extend its use throughout the seasons.
Lots of natural light is ideal but do you also need lighting for specific tasks, or a softer light for relaxation.
Although this is your place to get away from it all, Wifi is a must if it is to be used as an office, or even just a place to hide away with Spotify or Netflix.
If you are entertaining, you may want to consider a room with a wide open front, so people can spill onto a patio or decking area. A fire pit and some outdoor chairs are a fine addition to a garden room and extend its use considerably.