DD is 7 months tomorrow and has been having finger food since just before 6 months. She will eat anything she can pick up - toast, sandwiches, veg like broccoli, carrot sticks etc. We did the same with DS (both combined with purees) and kind of followed the baby led weaning advice for finger foods. We have always given chunks/ chip shaped fingers of food big enough to fit in their hands with a bit sticking out so that they can control what they do with it. They do gag at times but gaging helps them to learn control the food in their mouths so they won't choke. It can be scary but if you remember gaging isn't the same as choking and stay calm they can deal with most things. It also helps to learn what to do if they do choke so you are more confident.
Laura