Yes... Your Profile Cards module was the first one I purchased.   The Space/Group Category and Space parent will go a long way in  conveying some useful info to users. I thought about a short snippet of the Space/Group description might be useful, but I haven't even convinced myself that a description snippet would in all cases provide useful information.  You can already display hashtags from the description field, and that's probably already better than a description snippet could be.

I do use a custom field and selector list in my implementation of Spaces, but I realize adding custom field info to the card might be a little tricky.  For now, the fields you mentioned would be a good start and a huge help.