IME, people love to share food. And for those with dietary requirements, it means they know there will be things that they can eat for sure. And those that don't bake can buy things if they wish - veggie and dip platter, naice crisps, cheese, bread, salami etc. Savoury bake suggestions would be sausage rolls, mini pasties, cheese scones, mini quiches - oh, and chutneys!
Personally, I think that nice bread and ham/cheese/chicken separately is better than premade sarnies which are always a bit sad looking. Also lets people pick what they want
If you bought tea, milk, lemonade/dandelion and burdock/cream soda in glass bottles, jam, clotted cream, butter and made scones ahead of time and froze them, you'd have a bloomin good start to the tea. Oh, and poncey plates and cardboard cake stands.
Don't underestimate how much people like helping out at events. If I knew you, I'd be delighted to loan picnic blankets/ outdoor games/ decorations and to help organise the tea. And bake hugely. I love to bake, and its fab to get to do more