I highly recommend you shred your cheese yourself straight from the block as opposed to purchasing the pre-shredded stuff. Pre-shredded cheeses contain anti-caking agents which prevent them from melting down as well and may even make your cheese sauce grainy in texture.
You can cook some chicken breasts yourself for this recipe or use a pre-cooked rotisserie chicken from the grocery store. If you plan to cook some chicken for this dish, you may want to season it first. For example, a piece of boiled or poached chicken will be plain, but baked or steamed chicken will retain the seasoning flavors. If you are using a rotisserie chicken, it is already seasoned.
The half and half is an important part of why this dish is creamy and rich. I would not recommend substituting with regular milk here.