I started at 5.5 months and offered things like steamed carrot fingers, lightly steamed apple wedges or baked sweet potato or baked pear wedges. I avoided small round things like peas blueberries and cherry tomatoes because of the difficulty of picking up and also the additional choke hazard. But you can offer just about anything the family eats so long as your cook with no salt, sugar, honey, raw egg, whole nuts. It's ok to offer 'sloppy' foods too like mashed potato, fish pie etc as they can get fist fulls to their mouth. it's just about exploration and tasting so it doesn't matter if not much goes in.
There's a great thread for finger foods and BLW if you get short of ideas.