I hope this thread isn't looked at as bashing people with Depression or medication issues. What is best for the girl? Starting a relationship beyond a supportive friendship may be the worst thing for her now - more complexity in her life when she needs to concentrate on simplifying, healing, and making changes.
I will say this - some think that people NEED to be in a relationship, and that most problems can be fixed by finding the right mate, or finding that special person will solve most of their problems and make everything ok. This is COMPLETE bunk. People need to deal with THEMSELVES before they can deal with a mate and a relationship. Focusing on oneself is not selfishness, it is a prerequisite to a healthy relationship and to truly loving others. Ignoring personal issues by focusing on others or focusing on "the relationship" is a recipe for disaster, and only serves to distract one from the real problems. It's just a matter of time before unfixed issues resurface and leave the partner perplexed as to why his girl has changed, thinking "who is the real girl? the nice girl I met a year ago, or this devil she is now?"