If you want to be 100% gluten free be a little careful as the caeliacs I know have to be very vigilant about GF stuff that is made in factories that also process gluteny food (should be a warning on the label). Likewise they'll eat pre-packagef meat from a supermarket (that's come sealed straight from a meat packing plant) but not from a butchers or deli counter due to risk of cross contamination from pies/breadcrumbs ham etc.
The Caeliac Society has a very helpful list of safe foods.
It's not hard though, just check everything.
For finger foods, I'd do
GF bread and crackers but not too much as they aren't great
stuffed potato skins (lots of these with nice cold fillings, treat as an alternative to sandwiches, for example tuna mayo, smoked salmon and cream cheese, mushrooms in garlic cream sauce, roasted peppers with brie, roast beef and horseradish.)
cheeses (not from mixed deli counter),
make a tray of veg frittata and cut into cubes,
Co-op sausages,
chicken drumsticks,
salad, halved boiled eggs, tomatoes, olives,
GF crisps and dips.
And Little Moon mochi balls for desert as you can hold them to eat them and they are amazing!