I think the fairest and cleanest thing to do all round is just admit your not ready for a relationship.

Don't call it a break otherwise you run the risk of stringing them along and having to end it at a later date. Which could result in resentment and others getting involved. It's just messy and feels horrible for the person left waiting and wondering when your getting back together or when your going to call it quits.

I also wouldn't wait longer than absolutely necessary, regardless of what's going on in their life. Their situation might not improve for months in which time they will feel things are getting more serious whilst you are just waiting for the right time to get out.
They will have possibly opened up more and come more dependant leaving you finding it even harder to find a right time.

If you have only been together a few weeks chances are you can still get out now with minimum damage and disruption to the group. Might be awkward for a bit but will most likely blow over.

Hope you are able to keep your friendship, and maybe think about working on your struggle with relationships in time.
All the best.