Mix the white sugar, corn syrup, and salt in a large heavy-bottomed saucepan. Cover and cook over low heat until the sugar dissolves. Increase the heat and boil uncovered until the sugar turns a medium brown, about 7 minutes, but do not stir or swirl around to mix. Watch it carefully at the end, as it will go from caramel to burnt in no time. Put an oven mitt on the hand you will be using to stir in the butter, and heavy cream, and stand back to avoid splattering. Slowly and carefully, stir in the butter and the heavy cream. Remove the pan from the heat and stir in the vanilla. Cool slightly. Put the apples on a cookie sheet lined with lightly greased aluminum foil. Insert wooden sticks 3/4 of the way into the stem end of each apple. Dip each apple into the caramel and scrape the excess caramel from the bottoms using the side of the saucepan. Roll the apples in the desired toppings and arrange them on the aluminum foil. Serve.