He's probably getting close to ready for table foods. We started my little girl on table food at about 10 months. Try frozen peas or carrots (thawed of course)... small peices of bread or cheese... cottage cheese if he'll take it (my daughter doesn't seem to like the texture), small banana chunks, or avacado chunks, soft pears (I give her canned pears)... apples are great too, but remove peels from fruits to reduce gagging.
Cut everything into pieces no bigger than cheerios or peas. They should also be soft/cooked enough that you can easily smush them in your fingers. When my daughter was there, most of the gagging was casued by fruit peels or too big of peices. Their teeth are still pretty useless at this stage.
As far as finger foods goes, try Gerber yogurt bites. They's a little pricy, but my daugher loves them. Its freeze dried yogurt. She also really like the puffs as a first finger food.
Keep trying on the finger foods... keep offering them and eventually he'll get it. It could just be a texture thing for now... generally babies at that age refuse things based on texture more than on taste. Good luck!