How much sugar and vanilla extract should I use in 1/2 gallon of ice cream?
You're making what is (at least to Americans) called Philadelphia-style ice cream. The name makes it fairly easy to find the ratios. Checking three recipes:


http://www.culinate.com/books/collections/all_books/The+Perfect+Scoop/Vanilla+Ice+Cream
http://www.seriouseats.com/recipes/2014/12/30-minute-philadelphia-style-ice-cream-recipe.html
http://www.williams-sonoma.com/recipe/philadelphia-style-vanilla-ice-cream.html


all agree on ¾ sugar for 3 cups of dairy. So you'll likely want thrice that, or 2¼ c. sugar. (Sugar in ice cream isn't just for taste, it's also very important for texture.)

Then you'll want somewhere between 1–3 tablespoons of vanilla extract. This is a wide range, but actually vanilla ice creams available commercially in the US vary widely in the amount of vanilla flavor in them. I would recommend, if you remember what the melted ice cream tastes like (not frozen, as freezing will lessen the flavor somewhat), that you start with 1T, taste it, then mix in more as required.

Consider also a little bit of salt. Also, a 2:1 recipe of heavy cream to whole milk is common—saving you from having to purchase half and half.