I went to a baby weaning class and they recommended that finger foods should be started roughly when a baby has been eating purees or things for round about 3 weeks. The average baby doesnt get weaned until 6 month.
They recommend things like cucumber because its quite soft, cooked pasta shapes, hard boiled eggs cut into quarters, sticks of mild cheese.
The annabel karmel book is really good for ideas on all different stages of weaning. Try whacking the name into google and seeing what you find