Learn how to make homemade mayonnaise and aioli from scratch! It's easy and tastes worlds better than anything you'll buy at the store.
I find that using extra virgin olive oil results in a bitter aftertaste. If you can't find regular olive oil (or don't want to buy it), you can use a neutral-flavored oil, such as canola or grapeseed.
Since the eggs are consumed raw, it's safest to use pasteurized eggs, which have been heated to a temperature that kills many of the harmful bacteria.