Finger foods for Baby w/no Teeth?

I only know as much as my 8-month old has taught me, so sorry I can't offer toddler food suggestions. Thinking about this made me realize you ladies might have some insight on what I can feed my daughter Alena. She has no teeth but is at the stage where she insists on grabbing the spoon/bowl to feed herself. I need food large enough for her to successfully bring to her mouth, that won't be a choking hazard. We've not yet had luck with her being willing to eat cheerios, well-cooked broccoli stalks, cut up bananas or sweet potatoes (too mushy!). I might try tofu, small pieces of cheese and egg whites. I realize this could be a phase where Alena merely needs to explore the texture of food in her hand but I want to make sure she actually consumes something! Any other ideas?