If you are handing off to another editor for them to edit the same material, why not just give them your Project file and they can open directly? They will need the same media you started with however. This way you can ensure no quality loss whatsoever.
If you want to give them only the media that you have cut down I suppose you have the right idea. What are the sequence settings for the project you are working on? Did you change the sequence settings originally to match the media you were putting into it? What is the source material?
I usually setup my sequence as one of the various flavors of ProRes depending on the application and source material. ProRes 422 is usually a good bet but the file sizes can be large so it depends on how much material you are talking about.