Mess seems hard to avoid when just starting finger foods but a couple of suggestions, toast or bread, cheerios, and if you lo is doing meat here is a great recipe for "chicken fingers". Also check out the recipes under "Feeding Solids Foods" there are some really good ones there and some not so messy ones too!!
Chicken Fingers
2 chicken breasts (I use ground chicken)
1 eating apple (peeled and cored)
2 slices bread
1 medium onion
some fresh herbs of your choice (thyme works well)
flour
blitz apple in food processor, squeeze out excess juice, return to food processor and blitz with all other ingredients until really finely blended, shape into burgers or sausages, coat with a little flour, pan fry in a dribble of olive oil or bake in oven until cooked thru.
Variations could be pork, apple and sage, and lamb and mint