When it comes to knives and cheddar, I like mine nice and sharp. That said, feel free to use a cheese that makes sense for you! If you're more mild in taste, there's no shame in opting for a milder cheddar, or even subbing in some jack or mozzarella. As far as whether to choose white or yellow cheddar, that's entirely up to you! I used white this time because it was on sale so I stocked up. I have made this recipe for broccoli cheese soup with yellow cheddar too, and it was still delicious. Be warned, though. DON'T USE PRE-SHREDDED CHEESE. It has a coating that keeps it from melting into a big clump in the bag, but that coating keeps it from well... melting. Put in the little extra elbow grease and grate your own cheese. I promise you won't regret it.