Music is so huge, so many styles, so much music. You could spend your entire life just on one genre - classical, rock, country - and never even play/sing every piece once. Therefore, a great starting place for songs/pieces is doing WHAT YOU LOVE. Play and sing what you love at first so you're inspired and excited about all your music. It'll carry you a long way.
Most teachers don't care about your progress; they've got a few favorites and other students are just income. Find someone who's for you.