To answer the latter: Yes, you need vanilla bean paste. You need to buy a massive bottle on Amazon, store that stuff in your pantry next to the extracts this and that, and live the good life. Here's why:
As explained above, vanilla bean paste consists of the insides of the vanilla bean pod, a sugar-water syrup, and some sort of thickener. Extract, however, is an infusion of alcohol and water and vanilla (the alcohol cooks off when it's exposed to high heat, leaving the vanilla flavor behind). And the vanilla bean is, well, a bean. Basically, vanilla bean paste is the happy medium between extract and beans.
While the bean might be the pinnacle of vanilla-y flavor—bearing hundreds of thousands of flavorful specks ready to lend a hand to ice cream, cakes, banana breads, and muffins—they're expensive. Like, real expensive (like $10 a pop expensive). And if you buy a jar with a couple of vanilla beans and don't end up using both, the leftover bean will begin to lose its flavor with time. With paste, you get the intense flavor and aroma of the innards of a vanilla bean, but for the price of 1 or 2 beans you can get a whole jar of the stuff. There's no scraping of the pod and inevitably ending up with a good percentage of those precious little black dots left stuck to your knife or fingers--just some scooping with a teaspoon. And yes, bean paste has a much longer shelf life, up to 3 years if stored properly (in a cool, dry, dark place... like a kitchen cabinet). Vanilla bean paste can be used one-to-one for vanilla extract in most recipes.
Note--there's not a thing wrong with pure vanilla extract. If that's what's in your pantry, use it! But when it's time to buy another bottle, consider trying out paste instead. I find that it has a more intensely vanilla flavor thats comparable to using a bean. Plus, the paste gives you get all those pretty lil' flecks of vanilla bean. Specks are satisfying. Never underestimate the specks.