One of the worst disasters in a family get together is running out of food. For a perfect BBQ less is not more. It is better to have too much then too little.
The first trick is to consider the eating habits of the group. Are some big eaters? Are some small eaters?
The easiest way to come up with a perfect number is XXXXX figure two meat products for each person. That way it covers your big eaters. Should you have a majorities of people who like to eat (Like my family) You may wish to add another meat product for half the group. The children you will want to have one meat for. Though some children love hot dogs so I would have plenty of those on hand.
Based on a normal group of half and half I would say:
150 hamburgers, 200 hot dogs (Always have more hot dogs they make good cheap fillers you can also cut down on some hamburgers if you buy more hot dogs) and 50-75 Sausages (As children very seldom eat these)
Paper products you will need enough for 3 plates each (Meat, sides, desserts Plus extra for the kids who drop the plates) The same for silver wear, cups and napkins.
If you have a meat production wear house nearby you can get a very good price here verse your local store. Also consider Sam's as they sell in bulk.