I love a good BBQ and am 100% in agreement re burgers and sausages being a bit boring (although always always do a couple of packets of sausages for the kids - leftovers keep well).
Meat options I like:
Chicken thighs/drumsticks in marinade. Pre cook in the oven and then sear on the BBQ for the smokey/crispy exterior. Choose your marinade according to preference. Kids prefer tomato based ones but I personally like something a bit more lemony/herb/spicey.
Lamb is gorgeous on the BBQ. I have a new grill bbq so will be trying out butterflied leg of lamb this year. But that's quite ambitious. My go-to lamb options are either lamb chops marinaded in oil, lemon, thyme and garlic - simple and delicious (be generous so they can be piled on a platter) - or same marinade but skewers made with lamb neck (cut into chunks), peppers, aubergine, onion and tomatoes. If you do the skewers, you can serve them like that OR turn them into a meaty/veggie couscous salad by preparing couscous (flavoured to your preference) and then removing the meat and veg from skewers after they've been cooked and stir through.
Sides and salads:
One massive green salad is necessary. I usually make it quite elaborate - mixed types of lettuce, spring onions, chargrilled courgette slices or asparagus, cucumber. Top with feta cheese and toasted pine nuts. Dressing of choice but a vinaigrette of some sort is best I think.
A tomato salad is a good choice. I do mine with a chopped red onion, parsley and then sherry vinegar, olive oil and salt.
watermelon, feta, cucumber and chilli salad with a lime dressing is always a bit fun and colourful (cancel the chilli if lots of children around).
Baba ganoush works brilliantly as a side at a bbq, especially if you've done lamb. OR, bbq rounds of aubergine and mushrooms and create short stacks (two slices aubergine and two mushroom) using goats cheese and a sprinkle of fresh thyme between the layers then drizzle with some honey over the top. (good veggie option but make extra as meat eaters will have it as a side).
Still vaguely greek - tzatziki is great at a bbq and sits well with other meats. Make your own to get it really nice and don't forget to add a teaspoon of vinegar.
I like to do a big pot of baby potatoes as well as a selection of bread and rolls for people to choose their own carbohydrates. A nice pile of bread and rolls also looks nice on the table.