The point with FINGER food is that it has to be possible for the baby to pick it up and hold on to it by themselves. Most babies grab with their whole hand, and hold food clutched hard in their hand. Which means that anything smaller than the hand gets stuck in it - frustrating!!! And also, anything to mushy soft gets squashed! Think avocado and banana. At the beginning it is easier for them if it is bit firmer (but still soft), and long enough to have a "handle".
Yup, be careful about too small things and soft things on spoons in the early days. The gag reflex works much better if the baby gets to put something bigger in themselves and process it in their mouths!
For what it is worth, I am still worried about choking after nearly 4 months. I was terrified at the beginning and would only let DD eat when DH was around! Make sure you know how to deal with a choking baby, as babies can choke on anything. My LC/Well Baby-nurse told me babies are more likely to choke on liquids than anything else.