Just do loads of research. Loads. Research headlines like "xyz charity fined..." etc. Also, you can join Facebook groups for the specific thing you're wanting to donate to - autism, etc. And ask for stories of people helped by that specific charity.

Side note, Saint Judes Hospital is a really, really good cause and all profits go directly to the hospital. They take care of kids with cancer regardless of what their parents can afford.

Whatever you decide, whoever you decide to donate to, this is a really good thing you're doing. Don't let the logistics get in the way of that. God bless!