I want to make my own vanilla extract by infusing split vanilla pods in vodka for a couple months (using 8-10 beans per litre vodka). All the recipes I've read recommend vodka, because of its alcohol content (43%) and because it acts as a good neutral base for the vanilla flavour.
My question is: how good must the vodka be? I only cook with wines that are good enough to drink, but in this case, all I need is a neutral carrier for the vanilla, which I will add to recipes 1 tablespoon at a time. So can I get away with a cheap bottle of vodka, rather than grey goose or absolut? Or will a cheap vodka not be as 'neutral' in flavour? Thoughts?