My daughters lived on finger food when they were little. I found they would eat far more healthy food if it all looked nice and colourful, so I used to arrange on a huge plate an assortment of the following and let them pick:
fruit cut into bite sizes: apple, banana, strawberries, grapes, oranges, melon, pear, plums, apricots, satsuma, etc...
raw vegetables also cut into sticks or little pieces: carrots, cucumber, peppers, tomatoes, etc...
dried fruit and nuts: apricots, sultanas, raw unsalted cashews or almonds
slices of cheese, ham, quorn, wedges of egg
fingers of toast or bread with marmite, peanut butter, cheese spread, tartex, jam, lemon curd, honey, malted fruit loaf, pieces of currant bun or scone...
tortilla chips, frankfurters or other cooked sausage, pieces of quiche, sausage rolls
bowls of dip, humous, tzadziki, cheese and onion dip, guacamole, etc...
Occasional sweet treat of choc finger biscuits, pieces of cake etc...
My trick was to make it all look so appetising that they eat stuff they don't want when you say, 'how about an apple, or a peach?'
And it only takes five minutes to prepare.